From 04fdcf014b87974f01c541baf706c69e7392d0f8 Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Tue, 9 Dec 2025 16:55:52 -0500 Subject: [PATCH 01/21] Add small changes in `doe.rst` and a new local `.gitignore` script --- doc/OnlineDocs/.gitignore | 2 ++ .../explanation/analysis/doe/doe.rst | 35 +++++++++++++------ 2 files changed, 26 insertions(+), 11 deletions(-) create mode 100644 doc/OnlineDocs/.gitignore diff --git a/doc/OnlineDocs/.gitignore b/doc/OnlineDocs/.gitignore new file mode 100644 index 00000000000..405776298a5 --- /dev/null +++ b/doc/OnlineDocs/.gitignore @@ -0,0 +1,2 @@ +_build/ +api/ \ No newline at end of file diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index 6e77e55dfd6..549da534847 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -1,9 +1,11 @@ Pyomo.DoE ========= +**Pyomo.DoE** (Pyomo Design of Experiments) is a Python library for model-based design +of experiments using science-based models. -**Pyomo.DoE** (Pyomo Design of Experiments) is a Python library for model-based design of experiments using science-based models. - -Pyomo.DoE was developed by **Jialu Wang** and **Alexander W. Dowling** at the University of Notre Dame as part of the `Carbon Capture Simulation for Industry Impact (CCSI2) `_. +Pyomo.DoE was developed by **Jialu Wang** and **Alexander W. Dowling** at the +University of Notre Dame as part of the `Carbon Capture Simulation for Industry Impact +(CCSI2) `_. project, funded through the U.S. Department Of Energy Office of Fossil Energy. If you use Pyomo.DoE, please cite: @@ -15,28 +17,39 @@ AIChE Journal 68.12 (2022): e17813. `https://doi.org/10.1002/aic.17813` Methodology Overview --------------------- -Model-based Design of Experiments (MBDoE) is a technique to maximize the information gain of experiments by directly using science-based models with physically meaningful parameters. It is one key component in the model calibration and uncertainty quantification workflow shown below: +Model-based Design of Experiments (MBDoE) is a technique to maximize the information +gain of experiments by directly using science-based models with physically meaningful +parameters. It is one key component in the model calibration and uncertainty +quantification workflow shown below: .. figure:: flowchart.png :scale: 25 % - The exploratory analysis, parameter estimation, uncertainty analysis, and MBDoE are combined into an iterative framework to select, refine, and calibrate science-based mathematical models with quantified uncertainty. Currently, Pyomo.DoE focuses on increasing parameter precision. + The exploratory analysis, parameter estimation, uncertainty analysis, and MBDoE are + combined into an iterative framework to select, refine, and calibrate science-based + mathematical models with quantified uncertainty. Currently, Pyomo.DoE focuses on + increasing parameter precision. -Pyomo.DoE provides the exploratory analysis and MBDoE capabilities to the Pyomo ecosystem. The user provides one Pyomo model, a set of parameter nominal values, +Pyomo.DoE provides the exploratory analysis and MBDoE capabilities to the +Pyomo ecosystem. The user provides one Pyomo model, a set of parameter nominal values, the allowable design spaces for design variables, and the assumed observation error model. -During exploratory analysis, Pyomo.DoE checks if the model parameters can be inferred from the postulated measurements or preliminary data. +During exploratory analysis, Pyomo.DoE checks if the model parameters can be +inferred from the postulated measurements or preliminary data. MBDoE then recommends optimized experimental conditions for collecting more data. -Parameter estimation packages such as :ref:`Parmest ` can perform parameter estimation using the available data to infer values for parameters, +Parameter estimation packages such as :ref:`Parmest ` can perform +parameter estimation using the available data to infer values for parameters, and facilitate an uncertainty analysis to approximate the parameter covariance matrix. -If the parameter uncertainties are sufficiently small, the workflow terminates and returns the final model with quantified parametric uncertainty. -If not, MBDoE recommends optimized experimental conditions to generate new data. +If the parameter uncertainties are sufficiently small, the workflow terminates +and returns the final model with quantified parametric uncertainty. +If not, MBDoE recommends optimized experimental conditions to generate new data +that will maximize information gain and eventually reduce parameter uncertainty. Below is an overview of the type of optimization models Pyomo.DoE can accommodate: * Pyomo.DoE is suitable for optimization models of **continuous** variables * Pyomo.DoE can handle **equality constraints** defining state variables * Pyomo.DoE supports (Partial) Differential-Algebraic Equations (PDAE) models via Pyomo.DAE -* Pyomo.DoE also supports models with only algebraic constraints +* Pyomo.DoE also supports models with only algebraic equations The general form of a DAE problem that can be passed into Pyomo.DoE is shown below: From 5f2c58c28f5e78c624e56a8fabf5c0747d2c1df6 Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Thu, 11 Dec 2025 17:15:43 -0500 Subject: [PATCH 02/21] Update the `doe.rst` documentation --- .../explanation/analysis/doe/doe.rst | 71 +++++++++++++------ 1 file changed, 49 insertions(+), 22 deletions(-) diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index 549da534847..11485203105 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -79,7 +79,7 @@ where: * :math:`\mathbf{t} \in \mathbb{R}^{N_t \times 1}` is a union of all time sets. .. note:: - * Parameters and design variables should be defined as Pyomo ``Var`` components on the model to use ``direct_kaug`` mode, and can be defined as Pyomo ``Param`` object if not using ``direct_kaug``. + * Parameters and design variables should be defined as Pyomo ``Var`` components when building the model in ``Experiment`` Class so that users can use both ``ParmEst`` and ``Pyomo.DoE`` seamlessly. Based on the above notation, the form of the MBDoE problem addressed in Pyomo.DoE is shown below: @@ -88,14 +88,14 @@ Based on the above notation, the form of the MBDoE problem addressed in Pyomo.Do \begin{equation} \begin{aligned} - \underset{\boldsymbol{\varphi}}{\max} \quad & \Psi (\mathbf{M}(\mathbf{\hat{y}}, \boldsymbol{\varphi})) \\ - \text{s.t.} \quad & \mathbf{M}(\boldsymbol{\hat{\theta}}, \boldsymbol{\varphi}) = \sum_r^{N_r} \sum_{r'}^{N_r} \tilde{\sigma}_{(r,r')}\mathbf{Q}_r^\mathbf{T} \mathbf{Q}_{r'} + \mathbf{V}^{-1}_{\boldsymbol{\theta}}(\boldsymbol{\hat{\theta}}) \\ - & \dot{\mathbf{x}}(t) = \mathbf{f}(\mathbf{x}(t), \mathbf{z}(t), \mathbf{y}(t), \mathbf{u}(t), \overline{\mathbf{w}}, \boldsymbol{\theta}) \\ - & \mathbf{g}(\mathbf{x}(t), \mathbf{z}(t), \mathbf{y}(t), \mathbf{u}(t), \overline{\mathbf{w}},\boldsymbol{\theta})=\mathbf{0} \\ - & \mathbf{y} =\mathbf{h}(\mathbf{x}(t), \mathbf{z}(t), \mathbf{u}(t), \overline{\mathbf{w}},\boldsymbol{\theta}) \\ - & \mathbf{f}^{\mathbf{0}}\left(\dot{\mathbf{x}}\left(t_{0}\right), \mathbf{x}\left(t_{0}\right), \mathbf{z}(t_0), \mathbf{y}(t_0), \mathbf{u}\left(t_{0}\right), \overline{\mathbf{w}}, \boldsymbol{\theta})\right)=\mathbf{0} \\ - & \mathbf{g}^{\mathbf{0}}\left( \mathbf{x}\left(t_{0}\right),\mathbf{z}(t_0), \mathbf{y}(t_0), \mathbf{u}\left(t_{0}\right), \overline{\mathbf{w}}, \boldsymbol{\theta}\right)=\mathbf{0}\\ - &\mathbf{y}^{\mathbf{0}}\left(t_{0}\right)=\mathbf{h}\left(\mathbf{x}\left(t_{0}\right),\mathbf{z}(t_0), \mathbf{u}\left(t_{0}\right), \overline{\mathbf{w}}, \boldsymbol{\theta}\right) + \underset{\boldsymbol{\varphi}}{\max} \quad & \Psi (\mathbf{M}(\boldsymbol{\hat{\theta}}, \boldsymbol{\varphi})) \\ + \text{s.t.} \quad & \mathbf{M}(\boldsymbol{\hat{\theta}}, \boldsymbol{\varphi}) = \sum_r^{N_r} \sum_{r'}^{N_r} \tilde{\sigma}_{(r,r')}\mathbf{Q}_r^\mathbf{T} \mathbf{Q}_{r'} + \mathbf{V}_{\boldsymbol{\theta}}(\boldsymbol{\hat{\theta}})^{-1} \\ + & \dot{\mathbf{x}}(t) = \mathbf{f}(\mathbf{x}(t), \mathbf{z}(t), \mathbf{y}(t), \mathbf{u}(t), \overline{\mathbf{w}}, \boldsymbol{\hat{\theta}}) \\ + & \mathbf{g}(\mathbf{x}(t), \mathbf{z}(t), \mathbf{y}(t), \mathbf{u}(t), \overline{\mathbf{w}},\boldsymbol{\hat{\theta}})=\mathbf{0} \\ + & \mathbf{y} =\mathbf{h}(\mathbf{x}(t), \mathbf{z}(t), \mathbf{u}(t), \overline{\mathbf{w}},\boldsymbol{\hat{\theta}}) \\ + & \mathbf{f}^{\mathbf{0}}\left(\dot{\mathbf{x}}\left(t_{0}\right), \mathbf{x}\left(t_{0}\right), \mathbf{z}(t_0), \mathbf{y}(t_0), \mathbf{u}\left(t_{0}\right), \overline{\mathbf{w}}, \boldsymbol{\hat{\theta}})\right)=\mathbf{0} \\ + & \mathbf{g}^{\mathbf{0}}\left( \mathbf{x}\left(t_{0}\right),\mathbf{z}(t_0), \mathbf{y}(t_0), \mathbf{u}\left(t_{0}\right), \overline{\mathbf{w}}, \boldsymbol{\hat{\theta}}\right)=\mathbf{0}\\ + &\mathbf{y}^{\mathbf{0}}\left(t_{0}\right)=\mathbf{h}\left(\mathbf{x}\left(t_{0}\right),\mathbf{z}(t_0), \mathbf{u}\left(t_{0}\right), \overline{\mathbf{w}}, \boldsymbol{\hat{\theta}}\right) \end{aligned} \end{equation} @@ -107,7 +107,7 @@ where: * :math:`\Psi` is the design criteria to measure FIM. * :math:`\mathbf{V}_{\boldsymbol{\theta}}(\boldsymbol{\hat{\theta}})^{-1}` is the FIM of previous experiments. -Pyomo.DoE provides four design criteria :math:`\Psi` to measure the size of FIM: +Pyomo.DoE provides four design criteria :math:`\Psi` to measure the information in FIM: .. list-table:: Pyomo.DoE design criteria :header-rows: 1 @@ -116,8 +116,8 @@ Pyomo.DoE provides four design criteria :math:`\Psi` to measure the size of FIM * - Design criterion - Computation - Geometrical meaning - * - A-optimality - - :math:`\text{trace}({\mathbf{M}})` + * - A-optimality [#]_ + - :math:`\text{trace}({\mathbf{M}}^{-1})` - Dimensions of the enclosing box of the confidence ellipse * - D-optimality - :math:`\text{det}({\mathbf{M}})` @@ -129,25 +129,35 @@ Pyomo.DoE provides four design criteria :math:`\Psi` to measure the size of FIM - :math:`\text{cond}({\mathbf{M}})` - Ratio of the longest axis to the shortest axis of the confidence ellipse +.. [#] A-optimality is implemented as minimizing the trace of the inverse of FIM. + In order to solve problems of the above, Pyomo.DoE implements the 2-stage stochastic program. Please see Wang and Dowling (2022) for details. Pyomo.DoE Required Inputs -------------------------------- -The required input to the Pyomo.DoE solver is an ``Experiment`` object. The experiment object must have a ``get_labeled_model`` function which returns a Pyomo model with four ``Suffix`` components identifying the parts of the model used in MBDoE analysis. This is in line with the convention used in the parameter estimation tool, :ref:`Parmest `. The four ``Suffix`` components are: +The required input to the Pyomo.DoE solver is a subclass of the :ref:`Parmest ` ``Experiment`` class. The subclass must have a ``get_labeled_model`` method which returns a Pyomo model containing four Pyomo ``Suffix`` components identifying the parts of the model used in MBDoE analysis. This is in line with the convention used in the parameter estimation tool, :ref:`Parmest `. The four Pyomo ``Suffix`` components are: * ``experiment_inputs`` - The experimental design decisions * ``experiment_outputs`` - The values measured during the experiment * ``measurement_error`` - The error associated with individual values measured during the experiment * ``unknown_parameters`` - Those parameters in the model that are estimated using the measured values during the experiment -An example ``Experiment`` object that builds and labels the model is shown in the next few sections. +An example of the subclassed ``Experiment`` object that builds and labels the model is shown in the next few sections. Pyomo.DoE Usage Example ----------------------- -We illustrate the use of Pyomo.DoE using a reaction kinetics example (Wang and Dowling, 2022). -The Arrhenius equations model the temperature dependence of the reaction rate coefficient :math:`k_1, k_2`. Assuming a first-order reaction mechanism gives the reaction rate model. Further, we assume only species A is fed to the reactor. +We illustrate the use of Pyomo.DoE using a reaction kinetics example (Wang and Dowling, 2022). + +.. math:: + :nowrap: + + \begin{equation} + A \xrightarrow{k_1} B \xrightarrow{k_2} C + \end{equation} + +The Arrhenius equations model the temperature dependence of the reaction rate coefficient :math:`k_1, k_2`. Assuming a first-order reaction mechanism gives the reaction rate model. Further, we assume only species A is fed to the reactor. .. math:: :nowrap: @@ -174,14 +184,20 @@ The observation errors are assumed to be independent both in time and across mea Step 0: Import Pyomo and the Pyomo.DoE module and create an ``Experiment`` class ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ +.. note:: + + This example uses the data file ``result.json``, located in the Pyomo repository at: + ``pyomo/contrib/doe/examples/result.json``, which contains the nominal parameter values, and measurements for the reaction kinetics experiment. .. doctest:: - >>> # === Required import === + # === Required import === >>> import pyomo.environ as pyo >>> from pyomo.contrib.doe import DesignOfExperiments >>> import numpy as np +Subclass the :ref:`Parmest ` ``Experiment`` class to define the reaction kinetics experiment and build the Pyomo ConcreteModel. + .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_experiment.py :start-after: ======================== :end-before: End constructor definition @@ -189,7 +205,7 @@ Step 0: Import Pyomo and the Pyomo.DoE module and create an ``Experiment`` class Step 1: Define the Pyomo process model ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -The process model for the reaction kinetics problem is shown below. We build the model without any data or discretization. +The process model for the reaction kinetics problem is shown below. Here, we build the model without any data or discretization. .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_experiment.py :start-after: Create flexible model without data @@ -198,7 +214,7 @@ The process model for the reaction kinetics problem is shown below. We build the Step 2: Finalize the Pyomo process model ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -Here we add data to the model and finalize the discretization. This step is required before the model can be labeled. +Here, we add data to the model and finalize the discretization using a new method to the class. This step is required before the model can be labeled. .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_experiment.py :start-after: End equation definition @@ -207,7 +223,7 @@ Here we add data to the model and finalize the discretization. This step is requ Step 3: Label the information needed for DoE analysis ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -We label the four important groups as defined before. +We label the four important groups as defined before by adding a ``label_experiment`` method. .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_experiment.py :start-after: End model finalization @@ -226,16 +242,27 @@ Step 5: Exploratory analysis (Enumeration) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Exploratory analysis is suggested to enumerate the design space to check if the problem is identifiable, -i.e., ensure that D-, E-optimality metrics are not small numbers near zero, and Modified E-optimality is not a big number. +i.e., ensure that D-, E-optimality metrics are not small numbers near zero, and Modified E-optimality is not a big number. +Additionally, it helps to initialize the model for the optimal experimental design step. Pyomo.DoE can perform exploratory sensitivity analysis with the ``compute_FIM_full_factorial`` function. -The ``compute_FIM_full_factorial`` function generates a grid over the design space as specified by the user. Each grid point represents an MBDoE problem solved using ``compute_FIM`` method. In this way, sensitivity of the FIM over the design space can be evaluated. +The ``compute_FIM_full_factorial`` method generates a grid over the design space as specified by the user. Each grid point represents an MBDoE problem solved using ``compute_FIM`` method. In this way, sensitivity of the FIM over the design space can be evaluated. The following code executes the above problem description: .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py :start-after: Read in file + :end-before: Make design ranges to compute the full factorial design + :dedent: + +.. code-block:: python + + n_points_for_design = 9 # number of points for each design variable + +.. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py + :start-after: if compute_FIM_full_factorial: :end-before: End sensitivity analysis + :dedent: An example output of the code above, a design exploration for the initial concentration and temperature as experimental design variables with 9 values, produces the four figures summarized below: From 7fdc3a956d4a5206867891caba9442992ed87b54 Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Thu, 11 Dec 2025 18:11:22 -0500 Subject: [PATCH 03/21] Add new figure and update `doe.rst` --- .../analysis/doe/FIM_sensitivity.png | Bin 194054 -> 0 bytes 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zjudsFqaOM)Dwf?n_6i_|eFW$Z`fCdsXA3BgrRIhy1jL~HCHZ2`39@cR!@uJOOVQRE#4=scl`l)e-j(Fl-%>OcCqwPULKQXaXn0|} w0_+<}>Y%Zvm3WQ`a8fyG#pHKyXdh$J-|K$<)svZ>-&L>EoCGAEHOW0{{R3 literal 0 HcmV?d00001 diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index 11485203105..f8dd1ff1562 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -250,36 +250,122 @@ The ``compute_FIM_full_factorial`` method generates a grid over the design space The following code executes the above problem description: -.. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py - :start-after: Read in file - :end-before: Make design ranges to compute the full factorial design - :dedent: - .. code-block:: python - n_points_for_design = 9 # number of points for each design variable - -.. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py - :start-after: if compute_FIM_full_factorial: - :end-before: End sensitivity analysis - :dedent: - -An example output of the code above, a design exploration for the initial concentration and temperature as experimental design variables with 9 values, produces the four figures summarized below: - -.. figure:: FIM_sensitivity.png + # Read in file + DATA_DIR = pathlib.Path(__file__).parent + file_path = DATA_DIR / "result.json" + + with open(file_path) as f: + data_ex = json.load(f) + + # Put temperature control time points into correct format for reactor experiment + data_ex["control_points"] = { + float(k): v for k, v in data_ex["control_points"].items() + } + + # Create a ReactorExperiment object; data and discretization information are part + # of the constructor of this object + experiment = ReactorExperiment(data=data_ex, nfe=10, ncp=3) + + # Use a central difference, with step size 1e-3 + fd_formula = "central" + step_size = 1e-3 + + # Use the determinant objective with scaled sensitivity matrix + objective_option = "determinant" + scale_nominal_param_value = True + + # Create the DesignOfExperiments object + # We will not be passing any prior information in this example + # and allow the experiment object and the DesignOfExperiments + # call of ``run_doe`` perform model initialization. + doe_obj = DesignOfExperiments( + experiment, + fd_formula=fd_formula, + step=step_size, + objective_option=objective_option, + scale_constant_value=1, + scale_nominal_param_value=scale_nominal_param_value, + prior_FIM=None, + jac_initial=None, + fim_initial=None, + L_diagonal_lower_bound=1e-7, + solver=None, + tee=False, + get_labeled_model_args=None, + _Cholesky_option=True, + _only_compute_fim_lower=True, + ) + # Make design ranges to compute the full factorial design + design_ranges = { + "CA[0]": [1, 5, 9], + "T[0]": [300, 700, 9], + } + + # Compute the full factorial design with the sequential FIM calculation + doe_obj.compute_FIM_full_factorial( + design_ranges=design_ranges, method="sequential" + ) + # Save the results and plot the figures + figure_file_name = "example_reactor_compute_FIM" + + + # Plot the results + doe_obj.draw_factorial_figure( + sensitivity_design_variables=["CA[0]", "T[0]"], + fixed_design_variables={ + "T[0.125]": 300, + "T[0.25]": 300, + "T[0.375]": 300, + "T[0.5]": 300, + "T[0.625]": 300, + "T[0.75]": 300, + "T[0.875]": 300, + "T[1]": 300, + }, + title_text="Reactor Example", + xlabel_text="Concentration of A (M)", + ylabel_text="Initial Temperature (K)", + figure_file_name=figure_file_name, + log_scale=False, + ) + + +An example output of the code above, a design exploration for the initial +concentration and temperature as experimental design variables with 9 +values, produces the the four figures for four optimality criteria. +Only D-optimality is shown here. + +.. figure:: FIM_sensitivity_D-opt.png :scale: 50 % -A heatmap shows the change of the objective function, a.k.a. the experimental information content, in the design space. Horizontal and vertical axes are the two experimental design variables, while the color of each grid shows the experimental information content. For A optimality (top left subfigure), the figure shows that the most informative region is around :math:`C_{A0}=5.0` M, :math:`T=300.0` K, while the least informative region is around :math:`C_{A0}=1.0` M, :math:`T=700.0` K. +A heatmap shows the change of the objective function, a.k.a. the +experimental information content, in the design space. Horizontal +and vertical axes are the two experimental design variables, while +the color of each grid shows the experimental information content. +For D-optimality, the figure shows that the +most informative region is around :math:`C_{A0}=5.0` M, :math:`T=500.0` K with +a log-10 determinant of FIM being around 19, +while the least informative region is around :math:`C_{A0}=1.0` M, :math:`T=300.0` K, +with a log-10 determinant of FIM being around -5. + +``compute_FIM_full_factorial`` Step 6: Performing an optimal experimental design ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -In step 5, the DoE object was constructed to perform an exploratory sensitivity analysis. The same object can be used to design an optimal experiment with a single line of code. +In step 5, the DoE object was constructed to perform an exploratory sensitivity analysis. +The same object can be used to design an optimal experiment with a single +line of code. We can initialize the model with the result we obtained from +the exploratory analysis step to speed up convergence. .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py :start-after: Begin optimal DoE :end-before: Print out a results summary -When run, the optimal design is an initial concentration of 5.0 mol/L and an initial temperature of 494 K with all other temperatures being 300 K. The corresponding log-10 determinant of the FIM is 13.75 +When run, the optimal design is an initial concentration of 5.0 mol/L and +an initial temperature of 494 K with all other temperatures being 300 K. +The corresponding log-10 determinant of the FIM is 19.32. From 4c04187fcf4383bbd2174b9dedfbbf8f7248019b Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Fri, 12 Dec 2025 14:44:31 -0500 Subject: [PATCH 04/21] Add the new figures and new pseudo A-optimality and a code that is tested by running it. --- .../explanation/analysis/doe/doe.rst | 80 ++++++++++++------ ... => example_reactor_compute_FIM_D_opt.png} | Bin .../doe/example_reactor_compute_FIM_E_opt.png | Bin 0 -> 243808 bytes .../example_reactor_compute_FIM_ME_opt.png | Bin 0 -> 236395 bytes ...ample_reactor_compute_FIM_pseudo_A_opt.png | Bin 0 -> 275611 bytes 5 files changed, 52 insertions(+), 28 deletions(-) rename doc/OnlineDocs/explanation/analysis/doe/{FIM_sensitivity_D-opt.png => example_reactor_compute_FIM_D_opt.png} (100%) create mode 100644 doc/OnlineDocs/explanation/analysis/doe/example_reactor_compute_FIM_E_opt.png create mode 100644 doc/OnlineDocs/explanation/analysis/doe/example_reactor_compute_FIM_ME_opt.png create mode 100644 doc/OnlineDocs/explanation/analysis/doe/example_reactor_compute_FIM_pseudo_A_opt.png diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index f8dd1ff1562..a5c068a9845 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -5,7 +5,7 @@ of experiments using science-based models. Pyomo.DoE was developed by **Jialu Wang** and **Alexander W. Dowling** at the University of Notre Dame as part of the `Carbon Capture Simulation for Industry Impact -(CCSI2) `_. +(CCSI2) `_ project, funded through the U.S. Department Of Energy Office of Fossil Energy. If you use Pyomo.DoE, please cite: @@ -18,7 +18,7 @@ Methodology Overview --------------------- Model-based Design of Experiments (MBDoE) is a technique to maximize the information -gain of experiments by directly using science-based models with physically meaningful +gain from experiments by directly using science-based models with physically meaningful parameters. It is one key component in the model calibration and uncertainty quantification workflow shown below: @@ -36,7 +36,7 @@ the allowable design spaces for design variables, and the assumed observation er During exploratory analysis, Pyomo.DoE checks if the model parameters can be inferred from the postulated measurements or preliminary data. MBDoE then recommends optimized experimental conditions for collecting more data. -Parameter estimation packages such as :ref:`Parmest ` can perform +Parameter estimation packages such as :ref:`ParmEst ` can perform parameter estimation using the available data to infer values for parameters, and facilitate an uncertainty analysis to approximate the parameter covariance matrix. If the parameter uncertainties are sufficiently small, the workflow terminates @@ -79,7 +79,7 @@ where: * :math:`\mathbf{t} \in \mathbb{R}^{N_t \times 1}` is a union of all time sets. .. note:: - * Parameters and design variables should be defined as Pyomo ``Var`` components when building the model in ``Experiment`` Class so that users can use both ``ParmEst`` and ``Pyomo.DoE`` seamlessly. + * Parameters and design variables should be defined as Pyomo ``Var`` components when building the model in ``Experiment`` canlass so that users can use both ``ParmEst`` and ``Pyomo.DoE`` seamlessly. Based on the above notation, the form of the MBDoE problem addressed in Pyomo.DoE is shown below: @@ -116,8 +116,8 @@ Pyomo.DoE provides four design criteria :math:`\Psi` to measure the information * - Design criterion - Computation - Geometrical meaning - * - A-optimality [#]_ - - :math:`\text{trace}({\mathbf{M}}^{-1})` + * - Pseudo A-optimality + - :math:`\text{trace}({\mathbf{M}})` - Dimensions of the enclosing box of the confidence ellipse * - D-optimality - :math:`\text{det}({\mathbf{M}})` @@ -129,17 +129,20 @@ Pyomo.DoE provides four design criteria :math:`\Psi` to measure the information - :math:`\text{cond}({\mathbf{M}})` - Ratio of the longest axis to the shortest axis of the confidence ellipse -.. [#] A-optimality is implemented as minimizing the trace of the inverse of FIM. In order to solve problems of the above, Pyomo.DoE implements the 2-stage stochastic program. Please see Wang and Dowling (2022) for details. Pyomo.DoE Required Inputs -------------------------------- -The required input to the Pyomo.DoE solver is a subclass of the :ref:`Parmest ` ``Experiment`` class. The subclass must have a ``get_labeled_model`` method which returns a Pyomo model containing four Pyomo ``Suffix`` components identifying the parts of the model used in MBDoE analysis. This is in line with the convention used in the parameter estimation tool, :ref:`Parmest `. The four Pyomo ``Suffix`` components are: +The required input to the Pyomo.DoE is a subclass of the :ref:`ParmEst ` ``Experiment`` class. +The subclass must have a ``get_labeled_model`` method which returns a Pyomo `ConcreteModel` +containing four Pyomo ``Suffix`` components identifying the parts of the model used in +MBDoE analysis. This is in line with the convention used in the parameter estimation tool, + :ref:`ParmEst `. The four Pyomo ``Suffix`` components are: * ``experiment_inputs`` - The experimental design decisions * ``experiment_outputs`` - The values measured during the experiment -* ``measurement_error`` - The error associated with individual values measured during the experiment +* ``measurement_error`` - The error associated with individual values measured during the experiment. It is passed as a standard deviation or square root of the diagonal elements of the observation error covariance matrix. Pyomo.DoE currently assumes that the observation errors are Gaussain and independent both in time and across measurements. * ``unknown_parameters`` - Those parameters in the model that are estimated using the measured values during the experiment An example of the subclassed ``Experiment`` object that builds and labels the model is shown in the next few sections. @@ -177,7 +180,7 @@ The Arrhenius equations model the temperature dependence of the reaction rate co :math:`C_A(t), C_B(t), C_C(t)` are the time-varying concentrations of the species A, B, C, respectively. -:math:`k_1, k_2` are the rates for the two chemical reactions using an Arrhenius equation with activation energies :math:`E_1, E_2` and pre-exponential factors :math:`A_1, A_2`. +:math:`k_1, k_2` are the rate constants for the two chemical reactions using an Arrhenius equation with activation energies :math:`E_1, E_2` and pre-exponential factors :math:`A_1, A_2`. The goal of MBDoE is to optimize the experiment design variables :math:`\boldsymbol{\varphi} = (C_{A0}, T(t))`, where :math:`C_{A0},T(t)` are the initial concentration of species A and the time-varying reactor temperature, to maximize the precision of unknown model parameters :math:`\boldsymbol{\theta} = (A_1, E_1, A_2, E_2)` by measuring :math:`\mathbf{y}(t)=(C_A(t), C_B(t), C_C(t))`. The observation errors are assumed to be independent both in time and across measurements with a constant standard deviation of 1 M for each species. @@ -187,16 +190,21 @@ Step 0: Import Pyomo and the Pyomo.DoE module and create an ``Experiment`` class .. note:: This example uses the data file ``result.json``, located in the Pyomo repository at: - ``pyomo/contrib/doe/examples/result.json``, which contains the nominal parameter values, and measurements for the reaction kinetics experiment. + ``pyomo/contrib/doe/examples/result.json``, which contains the nominal parameter + values, and measurements for the reaction kinetics experiment. .. doctest:: # === Required import === >>> import pyomo.environ as pyo + >>> from pyomo.dae import ContinuousSet, DerivativeVar >>> from pyomo.contrib.doe import DesignOfExperiments + >>> from pyomo.contrib.parmest.experiment import Experiment + >>> import pathlib >>> import numpy as np + >>> import json -Subclass the :ref:`Parmest ` ``Experiment`` class to define the reaction kinetics experiment and build the Pyomo ConcreteModel. +Subclass the :ref:`ParmEst ` ``Experiment`` class to define the reaction kinetics experiment and build the Pyomo ConcreteModel. .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_experiment.py :start-after: ======================== @@ -223,7 +231,8 @@ Here, we add data to the model and finalize the discretization using a new metho Step 3: Label the information needed for DoE analysis ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -We label the four important groups as defined before by adding a ``label_experiment`` method. +We label the four important groups as Pyomo Suffix components as mentioned before by +adding a ``label_experiment`` method. .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_experiment.py :start-after: End model finalization @@ -232,7 +241,8 @@ We label the four important groups as defined before by adding a ``label_experim Step 4: Implement the ``get_labeled_model`` method ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -This method utilizes the previous 3 steps and is used by `Pyomo.DoE` to build the model to perform optimal experimental design. +This method utilizes the previous 3 steps and is used by `Pyomo.DoE` to build the model +to perform optimal experimental design. .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_experiment.py :start-after: End constructor definition @@ -245,7 +255,7 @@ Exploratory analysis is suggested to enumerate the design space to check if the i.e., ensure that D-, E-optimality metrics are not small numbers near zero, and Modified E-optimality is not a big number. Additionally, it helps to initialize the model for the optimal experimental design step. -Pyomo.DoE can perform exploratory sensitivity analysis with the ``compute_FIM_full_factorial`` function. +Pyomo.DoE can perform exploratory sensitivity analysis with the ``compute_FIM_full_factorial`` method. The ``compute_FIM_full_factorial`` method generates a grid over the design space as specified by the user. Each grid point represents an MBDoE problem solved using ``compute_FIM`` method. In this way, sensitivity of the FIM over the design space can be evaluated. The following code executes the above problem description: @@ -334,23 +344,34 @@ The following code executes the above problem description: An example output of the code above, a design exploration for the initial concentration and temperature as experimental design variables with 9 -values, produces the the four figures for four optimality criteria. -Only D-optimality is shown here. +values for each, produces the the four figures for four optimality criteria as shown below: -.. figure:: FIM_sensitivity_D-opt.png - :scale: 50 % +|plot1| |plot2| -A heatmap shows the change of the objective function, a.k.a. the +|plot3| |plot4| + +.. |plot1| image:: example_reactor_compute_FIM_D_opt.png + :width: 48 % + +.. |plot2| image:: example_reactor_compute_FIM_pseudo_A_opt.png + :width: 48 % + +.. |plot3| image:: example_reactor_compute_FIM_E_opt.png + :width: 48 % + +.. |plot4| image:: example_reactor_compute_FIM_ME_opt.png + :width: 48 % + +The heatmaps show the values of the objective functions, a.k.a. the experimental information content, in the design space. Horizontal and vertical axes are the two experimental design variables, while the color of each grid shows the experimental information content. -For D-optimality, the figure shows that the +For D-optimality (upper left subplot), the figure shows that the most informative region is around :math:`C_{A0}=5.0` M, :math:`T=500.0` K with -a log-10 determinant of FIM being around 19, +a :math:`\log_{10}` determinant of FIM being around 19, while the least informative region is around :math:`C_{A0}=1.0` M, :math:`T=300.0` K, -with a log-10 determinant of FIM being around -5. +with a :math:`\log_{10}` determinant of FIM being around -5. -``compute_FIM_full_factorial`` Step 6: Performing an optimal experimental design ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ @@ -360,12 +381,15 @@ The same object can be used to design an optimal experiment with a single line of code. We can initialize the model with the result we obtained from the exploratory analysis step to speed up convergence. -.. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py - :start-after: Begin optimal DoE - :end-before: Print out a results summary +.. code-block:: python + + doe_obj.run_doe() + # Print the optimal design and corresponding objective value + print(doe_obj.results) + When run, the optimal design is an initial concentration of 5.0 mol/L and an initial temperature of 494 K with all other temperatures being 300 K. -The corresponding log-10 determinant of the FIM is 19.32. +The corresponding :math:`\log_{10}` determinant of the FIM is 19.32. diff --git a/doc/OnlineDocs/explanation/analysis/doe/FIM_sensitivity_D-opt.png b/doc/OnlineDocs/explanation/analysis/doe/example_reactor_compute_FIM_D_opt.png similarity index 100% rename from doc/OnlineDocs/explanation/analysis/doe/FIM_sensitivity_D-opt.png rename to 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zU)ZZ5h+JrmbwKex3ae1hyri{<^Zyq!m(SwgzkiR+HIZ&OYZ{<3x-$6_&JQFv2=K*K zV|yszVsw@+W}Blh9xE`b6XJ;zS%%JeeY5nxFFo_WFA77aLr|{&yb*(=CW^~pp~_=p yi!%-0HX7$qLDvb^FHrapZM~Ah?69KD^*?$PTb}(p+eKzPEsPD!DEa!%C;lIzDdmCy literal 0 HcmV?d00001 From ce6e8ccd8ac0741d881cd81f44bed52e519eafed Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Fri, 9 Jan 2026 10:47:38 -0500 Subject: [PATCH 05/21] Fix `ParmEst` to `Parmest` and add `A-optimality` --- doc/OnlineDocs/explanation/analysis/doe/doe.rst | 15 +++++++++------ 1 file changed, 9 insertions(+), 6 deletions(-) diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index a5c068a9845..fdf461263dc 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -36,7 +36,7 @@ the allowable design spaces for design variables, and the assumed observation er During exploratory analysis, Pyomo.DoE checks if the model parameters can be inferred from the postulated measurements or preliminary data. MBDoE then recommends optimized experimental conditions for collecting more data. -Parameter estimation packages such as :ref:`ParmEst ` can perform +Parameter estimation packages such as :ref:`Parmest ` can perform parameter estimation using the available data to infer values for parameters, and facilitate an uncertainty analysis to approximate the parameter covariance matrix. If the parameter uncertainties are sufficiently small, the workflow terminates @@ -79,7 +79,7 @@ where: * :math:`\mathbf{t} \in \mathbb{R}^{N_t \times 1}` is a union of all time sets. .. note:: - * Parameters and design variables should be defined as Pyomo ``Var`` components when building the model in ``Experiment`` canlass so that users can use both ``ParmEst`` and ``Pyomo.DoE`` seamlessly. + * Parameters and design variables should be defined as Pyomo ``Var`` components when building the model in ``Experiment`` canlass so that users can use both ``Parmest`` and ``Pyomo.DoE`` seamlessly. Based on the above notation, the form of the MBDoE problem addressed in Pyomo.DoE is shown below: @@ -116,9 +116,12 @@ Pyomo.DoE provides four design criteria :math:`\Psi` to measure the information * - Design criterion - Computation - Geometrical meaning + * - A-optimality + - :math:`\text{trace}({\mathbf{M}}^{-1})` + - Sum of the dimensions of the confidence ellipse * - Pseudo A-optimality - :math:`\text{trace}({\mathbf{M}})` - - Dimensions of the enclosing box of the confidence ellipse + - Dimensions of the enclosing box of the inverse of the confidence ellipse * - D-optimality - :math:`\text{det}({\mathbf{M}})` - Volume of the confidence ellipse @@ -134,11 +137,11 @@ In order to solve problems of the above, Pyomo.DoE implements the 2-stage stocha Pyomo.DoE Required Inputs -------------------------------- -The required input to the Pyomo.DoE is a subclass of the :ref:`ParmEst ` ``Experiment`` class. +The required input to the Pyomo.DoE is a subclass of the :ref:`Parmest ` ``Experiment`` class. The subclass must have a ``get_labeled_model`` method which returns a Pyomo `ConcreteModel` containing four Pyomo ``Suffix`` components identifying the parts of the model used in MBDoE analysis. This is in line with the convention used in the parameter estimation tool, - :ref:`ParmEst `. The four Pyomo ``Suffix`` components are: + :ref:`Parmest `. The four Pyomo ``Suffix`` components are: * ``experiment_inputs`` - The experimental design decisions * ``experiment_outputs`` - The values measured during the experiment @@ -204,7 +207,7 @@ Step 0: Import Pyomo and the Pyomo.DoE module and create an ``Experiment`` class >>> import numpy as np >>> import json -Subclass the :ref:`ParmEst ` ``Experiment`` class to define the reaction kinetics experiment and build the Pyomo ConcreteModel. +Subclass the :ref:`Parmest ` ``Experiment`` class to define the reaction kinetics experiment and build the Pyomo ConcreteModel. .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_experiment.py :start-after: ======================== From f832acd558412d81c9eb1a06525c68d084c31ac2 Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Fri, 9 Jan 2026 11:26:51 -0500 Subject: [PATCH 06/21] Add `A-optimality` --- .../explanation/analysis/doe/doe.rst | 19 ++++++++++++------ .../doe/example_reactor_compute_FIM_A_opt.png | Bin 0 -> 243831 bytes 2 files changed, 13 insertions(+), 6 deletions(-) create mode 100644 doc/OnlineDocs/explanation/analysis/doe/example_reactor_compute_FIM_A_opt.png diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index fdf461263dc..a20e3fbb279 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -118,7 +118,7 @@ Pyomo.DoE provides four design criteria :math:`\Psi` to measure the information - Geometrical meaning * - A-optimality - :math:`\text{trace}({\mathbf{M}}^{-1})` - - Sum of the dimensions of the confidence ellipse + - Dimensions of the enclosing box of the confidence ellipse * - Pseudo A-optimality - :math:`\text{trace}({\mathbf{M}})` - Dimensions of the enclosing box of the inverse of the confidence ellipse @@ -353,27 +353,34 @@ values for each, produces the the four figures for four optimality criteria as s |plot3| |plot4| +|plot5| + .. |plot1| image:: example_reactor_compute_FIM_D_opt.png :width: 48 % -.. |plot2| image:: example_reactor_compute_FIM_pseudo_A_opt.png +.. |plot2| image:: example_reactor_compute_FIM_A_opt.png + :width: 48 % + +.. |plot3| image:: example_reactor_compute_FIM_pseudo_A_opt.png :width: 48 % -.. |plot3| image:: example_reactor_compute_FIM_E_opt.png +.. |plot4| image:: example_reactor_compute_FIM_E_opt.png :width: 48 % -.. |plot4| image:: example_reactor_compute_FIM_ME_opt.png +.. |plot5| image:: example_reactor_compute_FIM_ME_opt.png :width: 48 % The heatmaps show the values of the objective functions, a.k.a. the experimental information content, in the design space. Horizontal and vertical axes are the two experimental design variables, while the color of each grid shows the experimental information content. -For D-optimality (upper left subplot), the figure shows that the +For example, the D-optimality (upper left subplot) heatmap figure shows that the most informative region is around :math:`C_{A0}=5.0` M, :math:`T=500.0` K with a :math:`\log_{10}` determinant of FIM being around 19, while the least informative region is around :math:`C_{A0}=1.0` M, :math:`T=300.0` K, -with a :math:`\log_{10}` determinant of FIM being around -5. +with a :math:`\log_{10}` determinant of FIM being around -5. For D-, Pseudo A-, and +E-optimality we want to maximize the objective values, while for A- and Modified +E-optimality we want to minimize the objective values. 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zo^NX{W%|vwWRR?{;B2+1Wt?^1Cd04n@mwwn4u0@BjNhRuebAR;L%7_q>_P zBDO}ap)oIYi94lzI}jH3rnC`!=LSk2uKQdV5Yf5jVUODeFD#6nG~#$+rbrLA{As3H Jis{mw{{vLWBpm<% literal 0 HcmV?d00001 From 55af60a06433623190207341a9aadc853b6144de Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Fri, 9 Jan 2026 11:42:54 -0500 Subject: [PATCH 07/21] Remove local `gitignore` --- doc/OnlineDocs/.gitignore | 2 -- 1 file changed, 2 deletions(-) delete mode 100644 doc/OnlineDocs/.gitignore diff --git a/doc/OnlineDocs/.gitignore b/doc/OnlineDocs/.gitignore deleted file mode 100644 index 405776298a5..00000000000 --- a/doc/OnlineDocs/.gitignore +++ /dev/null @@ -1,2 +0,0 @@ -_build/ -api/ \ No newline at end of file From ee519c9c381bf4f4c74ac119450502d913c509ab Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Mon, 12 Jan 2026 12:17:12 -0500 Subject: [PATCH 08/21] Add `literalinclude` instead of copy-pasted code. --- .../explanation/analysis/doe/doe.rst | 121 +++++------------- 1 file changed, 33 insertions(+), 88 deletions(-) diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index a20e3fbb279..c3f734d9cdf 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -263,87 +263,32 @@ The ``compute_FIM_full_factorial`` method generates a grid over the design space The following code executes the above problem description: -.. code-block:: python - - # Read in file - DATA_DIR = pathlib.Path(__file__).parent - file_path = DATA_DIR / "result.json" - - with open(file_path) as f: - data_ex = json.load(f) - - # Put temperature control time points into correct format for reactor experiment - data_ex["control_points"] = { - float(k): v for k, v in data_ex["control_points"].items() - } - - # Create a ReactorExperiment object; data and discretization information are part - # of the constructor of this object - experiment = ReactorExperiment(data=data_ex, nfe=10, ncp=3) - - # Use a central difference, with step size 1e-3 - fd_formula = "central" - step_size = 1e-3 - - # Use the determinant objective with scaled sensitivity matrix - objective_option = "determinant" - scale_nominal_param_value = True - - # Create the DesignOfExperiments object - # We will not be passing any prior information in this example - # and allow the experiment object and the DesignOfExperiments - # call of ``run_doe`` perform model initialization. - doe_obj = DesignOfExperiments( - experiment, - fd_formula=fd_formula, - step=step_size, - objective_option=objective_option, - scale_constant_value=1, - scale_nominal_param_value=scale_nominal_param_value, - prior_FIM=None, - jac_initial=None, - fim_initial=None, - L_diagonal_lower_bound=1e-7, - solver=None, - tee=False, - get_labeled_model_args=None, - _Cholesky_option=True, - _only_compute_fim_lower=True, - ) - # Make design ranges to compute the full factorial design - design_ranges = { - "CA[0]": [1, 5, 9], - "T[0]": [300, 700, 9], - } - - # Compute the full factorial design with the sequential FIM calculation - doe_obj.compute_FIM_full_factorial( - design_ranges=design_ranges, method="sequential" - ) - # Save the results and plot the figures - figure_file_name = "example_reactor_compute_FIM" - - - # Plot the results - doe_obj.draw_factorial_figure( - sensitivity_design_variables=["CA[0]", "T[0]"], - fixed_design_variables={ - "T[0.125]": 300, - "T[0.25]": 300, - "T[0.375]": 300, - "T[0.5]": 300, - "T[0.625]": 300, - "T[0.75]": 300, - "T[0.875]": 300, - "T[1]": 300, - }, - title_text="Reactor Example", - xlabel_text="Concentration of A (M)", - ylabel_text="Initial Temperature (K)", - figure_file_name=figure_file_name, - log_scale=False, - ) - +.. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py + :language: python + :start-after: # Read in file + :end-before: if compute_FIM_full_factorial: + :dedent: 4 + :prepend: # Read in file + +.. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py + :language: python + :start-after: if compute_FIM_full_factorial: + :end-before: if plot_factorial_results: + :dedent: 8 + :prepend: n_points_for_design = 9 + +.. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py + :language: python + :start-after: if save_plots: + :end-before: else: + :dedent: 12 + +.. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py + :language: python + :start-after: # Plot the results + :end-before: ########################### + :dedent: 8 + :prepend: # Plot the results An example output of the code above, a design exploration for the initial concentration and temperature as experimental design variables with 9 @@ -391,14 +336,14 @@ The same object can be used to design an optimal experiment with a single line of code. We can initialize the model with the result we obtained from the exploratory analysis step to speed up convergence. -.. code-block:: python +.. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py + :language: python + :start-after: if run_optimal_doe: + :end-before: ################### + :dedent: 8 + :prepend: # Run optimal DoE - doe_obj.run_doe() - # Print the optimal design and corresponding objective value - print(doe_obj.results) - - -When run, the optimal design is an initial concentration of 5.0 mol/L and +After running this code, the optimal design is an initial concentration of 5.0 mol/L and an initial temperature of 494 K with all other temperatures being 300 K. The corresponding :math:`\log_{10}` determinant of the FIM is 19.32. From 4a9f2c8f0c2e0bc9c5cace8ec2b7151704c052ec Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Mon, 12 Jan 2026 13:39:15 -0500 Subject: [PATCH 09/21] Add the example as a single block of code instead of multiple blocks of segmented code. --- .../explanation/analysis/doe/doe.rst | 73 ++++++++----------- 1 file changed, 32 insertions(+), 41 deletions(-) diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index c3f734d9cdf..c8fc50c1b65 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -140,8 +140,8 @@ Pyomo.DoE Required Inputs The required input to the Pyomo.DoE is a subclass of the :ref:`Parmest ` ``Experiment`` class. The subclass must have a ``get_labeled_model`` method which returns a Pyomo `ConcreteModel` containing four Pyomo ``Suffix`` components identifying the parts of the model used in -MBDoE analysis. This is in line with the convention used in the parameter estimation tool, - :ref:`Parmest `. The four Pyomo ``Suffix`` components are: +MBDoE analysis. This is in line with the convention used in the parameter estimation tool, +:ref:`Parmest `. The four Pyomo ``Suffix`` components are: * ``experiment_inputs`` - The experimental design decisions * ``experiment_outputs`` - The values measured during the experiment @@ -254,45 +254,39 @@ to perform optimal experimental design. Step 5: Exploratory analysis (Enumeration) ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -Exploratory analysis is suggested to enumerate the design space to check if the problem is identifiable, +After creating the subclass of the ``Experiment`` class, exploratory analysis is +suggested to enumerate the design space to check if the problem is identifiable, i.e., ensure that D-, E-optimality metrics are not small numbers near zero, and Modified E-optimality is not a big number. Additionally, it helps to initialize the model for the optimal experimental design step. Pyomo.DoE can perform exploratory sensitivity analysis with the ``compute_FIM_full_factorial`` method. -The ``compute_FIM_full_factorial`` method generates a grid over the design space as specified by the user. Each grid point represents an MBDoE problem solved using ``compute_FIM`` method. In this way, sensitivity of the FIM over the design space can be evaluated. +The ``compute_FIM_full_factorial`` method generates a grid over the design space as specified by the user. +Each grid point represents an MBDoE problem solved using ``compute_FIM`` method. +In this way, sensitivity of the FIM over the design space can be evaluated. +Pyomo.DoE supports plotting the results from ``compute_FIM_full_factorial`` method +with the ``draw_factorial_figure`` method. -The following code executes the above problem description: +The following code defines the ``run_reactor_doe`` function. This function encapsulates +the workflow for both sensitivity analysis (Step 5) and optimal design (Step 6). .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py - :language: python - :start-after: # Read in file - :end-before: if compute_FIM_full_factorial: - :dedent: 4 - :prepend: # Read in file + :language: python + :start-after: # This software is distributed under the 3-clause BSD License. + :end-before: if __name__ == "__main__": + :linenos: -.. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py - :language: python - :start-after: if compute_FIM_full_factorial: - :end-before: if plot_factorial_results: - :dedent: 8 - :prepend: n_points_for_design = 9 +After defining the function, we will call it to perform the exploratory analysis and +the optimal experimental design. .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py :language: python - :start-after: if save_plots: - :end-before: else: - :dedent: 12 - -.. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py - :language: python - :start-after: # Plot the results - :end-before: ########################### - :dedent: 8 - :prepend: # Plot the results + :start-after: if __name__ == "__main__": + :dedent: 4 -An example output of the code above, a design exploration for the initial -concentration and temperature as experimental design variables with 9 -values for each, produces the the four figures for four optimality criteria as shown below: +A design exploration for the initial concentration and temperature as experimental +design variables with 9 values for each, produces the the five figures for +five optimality criteria using ``compute_FIM_full_factorial`` and +``draw_factorial_figure`` methods as shown below: |plot1| |plot2| @@ -331,19 +325,16 @@ E-optimality we want to minimize the objective values. Step 6: Performing an optimal experimental design ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -In step 5, the DoE object was constructed to perform an exploratory sensitivity analysis. -The same object can be used to design an optimal experiment with a single -line of code. We can initialize the model with the result we obtained from -the exploratory analysis step to speed up convergence. +In Step 5, we defined the ``run_reactor_doe`` function. This function constructs +the DoE object and performs the exploratory sensitivity analysis. By default, +it also proceeds immediately to the optimal experimental design step +(applying ``run_doe`` on the ``DesignOfExperiments`` object). +We can initialize the model with the result we obtained from the exploratory +analysis (optimal point from the heatmaps) to help the optimal design step to speed +up convergence. However, implementation of this initialization is not shown here. -.. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_example.py - :language: python - :start-after: if run_optimal_doe: - :end-before: ################### - :dedent: 8 - :prepend: # Run optimal DoE - -After running this code, the optimal design is an initial concentration of 5.0 mol/L and +After applying ``run_doe`` on the ``DesignOfExperiments`` object, +the optimal design is an initial concentration of 5.0 mol/L and an initial temperature of 494 K with all other temperatures being 300 K. The corresponding :math:`\log_{10}` determinant of the FIM is 19.32. From ab28e82cb80b0d188af8b13de551622c2be53ae9 Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Fri, 6 Feb 2026 16:18:37 -0500 Subject: [PATCH 10/21] Add contribution and minor text correction --- .../explanation/analysis/doe/doe.rst | 41 ++++++++++++------- 1 file changed, 26 insertions(+), 15 deletions(-) diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index c8fc50c1b65..eb952b7aecb 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -3,10 +3,15 @@ Pyomo.DoE **Pyomo.DoE** (Pyomo Design of Experiments) is a Python library for model-based design of experiments using science-based models. -Pyomo.DoE was developed by **Jialu Wang** and **Alexander W. Dowling** at the +Pyomo.DoE was originally created by **Jialu Wang** and **Alexander W. Dowling** at the University of Notre Dame as part of the `Carbon Capture Simulation for Industry Impact (CCSI2) `_ -project, funded through the U.S. Department Of Energy Office of Fossil Energy. +project, funded through the U.S. Department Of Energy Office of Fossil Energy with +assistance from **John Siirola**, **Bethany Nicholson**, **Miranda Mundt**,and **Hailey Lynch**. +Significant improvements and extensions were contributed by **Dan Laky**, and +**Shuvashish Mondal** with funding from the +`Process Optimization & Modeling for Minerals Sustainability (PrOMMiS) `_ +and the `University of Notre Dame `_. If you use Pyomo.DoE, please cite: @@ -48,7 +53,7 @@ Below is an overview of the type of optimization models Pyomo.DoE can accommodat * Pyomo.DoE is suitable for optimization models of **continuous** variables * Pyomo.DoE can handle **equality constraints** defining state variables -* Pyomo.DoE supports (Partial) Differential-Algebraic Equations (PDAE) models via Pyomo.DAE +* Pyomo.DoE supports (Partial) Differential-Algebraic Equations (PDAE) models via :ref:`Pyomo.DAE ` * Pyomo.DoE also supports models with only algebraic equations The general form of a DAE problem that can be passed into Pyomo.DoE is shown below: @@ -60,7 +65,7 @@ The general form of a DAE problem that can be passed into Pyomo.DoE is shown bel \dot{\mathbf{x}}(t) = \mathbf{f}(\mathbf{x}(t), \mathbf{z}(t), \mathbf{y}(t), \mathbf{u}(t), \overline{\mathbf{w}}, \boldsymbol{\theta}) \\ \mathbf{g}(\mathbf{x}(t), \mathbf{z}(t), \mathbf{y}(t), \mathbf{u}(t), \overline{\mathbf{w}},\boldsymbol{\theta})=\mathbf{0} \\ \mathbf{y} =\mathbf{h}(\mathbf{x}(t), \mathbf{z}(t), \mathbf{u}(t), \overline{\mathbf{w}},\boldsymbol{\theta}) \\ - \mathbf{f}^{\mathbf{0}}\left(\dot{\mathbf{x}}\left(t_{0}\right), \mathbf{x}\left(t_{0}\right), \mathbf{z}(t_0), \mathbf{y}(t_0), \mathbf{u}\left(t_{0}\right), \overline{\mathbf{w}}, \boldsymbol{\theta})\right)=\mathbf{0} \\ + \mathbf{f}^{\mathbf{0}}\left(\dot{\mathbf{x}}\left(t_{0}\right), \mathbf{x}\left(t_{0}\right), \mathbf{z}(t_0), \mathbf{y}(t_0), \mathbf{u}\left(t_{0}\right), \overline{\mathbf{w}}, \boldsymbol{\theta}\right)=\mathbf{0} \\ \mathbf{g}^{\mathbf{0}}\left( \mathbf{x}\left(t_{0}\right),\mathbf{z}(t_0), \mathbf{y}(t_0), \mathbf{u}\left(t_{0}\right), \overline{\mathbf{w}}, \boldsymbol{\theta}\right)=\mathbf{0}\\ \mathbf{y}^{\mathbf{0}}\left(t_{0}\right)=\mathbf{h}\left(\mathbf{x}\left(t_{0}\right),\mathbf{z}(t_0), \mathbf{u}\left(t_{0}\right), \overline{\mathbf{w}}, \boldsymbol{\theta}\right) \end{array}\] @@ -79,7 +84,9 @@ where: * :math:`\mathbf{t} \in \mathbb{R}^{N_t \times 1}` is a union of all time sets. .. note:: - * Parameters and design variables should be defined as Pyomo ``Var`` components when building the model in ``Experiment`` canlass so that users can use both ``Parmest`` and ``Pyomo.DoE`` seamlessly. + * Parameters and design variables should be defined as Pyomo ``Var`` components + when building the model using the ``Experiment`` class so that users can use both + ``Parmest`` and ``Pyomo.DoE`` seamlessly. Based on the above notation, the form of the MBDoE problem addressed in Pyomo.DoE is shown below: @@ -104,10 +111,10 @@ where: * :math:`\boldsymbol{\varphi}` are design variables, which are manipulated to maximize the information content of experiments. It should consist of one or more of :math:`\mathbf{u}(t), \mathbf{y}^{\mathbf{0}}({t_0}),\overline{\mathbf{w}}`. With a proper model formulation, the timepoints for control or measurements :math:`\mathbf{t}` can also be degrees of freedom. * :math:`\mathbf{M}` is the Fisher information matrix (FIM), estimated as the inverse of the covariance matrix of parameter estimates :math:`\boldsymbol{\hat{\theta}}`. A large FIM indicates more information contained in the experiment for parameter estimation. * :math:`\mathbf{Q}` is the dynamic sensitivity matrix, containing the partial derivatives of :math:`\mathbf{y}` with respect to :math:`\boldsymbol{\theta}`. -* :math:`\Psi` is the design criteria to measure FIM. +* :math:`\Psi` is the scalar design criteria to measure the information content in FIM. * :math:`\mathbf{V}_{\boldsymbol{\theta}}(\boldsymbol{\hat{\theta}})^{-1}` is the FIM of previous experiments. -Pyomo.DoE provides four design criteria :math:`\Psi` to measure the information in FIM: +Pyomo.DoE provides five design criteria :math:`\Psi` to measure the information in FIM: .. list-table:: Pyomo.DoE design criteria :header-rows: 1 @@ -207,7 +214,8 @@ Step 0: Import Pyomo and the Pyomo.DoE module and create an ``Experiment`` class >>> import numpy as np >>> import json -Subclass the :ref:`Parmest ` ``Experiment`` class to define the reaction kinetics experiment and build the Pyomo ConcreteModel. +Subclass the :ref:`Parmest ` ``Experiment`` class to define the reaction +kinetics experiment and build the Pyomo ConcreteModel. .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_experiment.py :start-after: ======================== @@ -216,7 +224,8 @@ Subclass the :ref:`Parmest ` ``Experiment`` class to define the reactio Step 1: Define the Pyomo process model ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -The process model for the reaction kinetics problem is shown below. Here, we build the model without any data or discretization. +The process model for the reaction kinetics problem is shown below. Here, we build +the model without any data or discretization. .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_experiment.py :start-after: Create flexible model without data @@ -225,7 +234,8 @@ The process model for the reaction kinetics problem is shown below. Here, we bui Step 2: Finalize the Pyomo process model ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ -Here, we add data to the model and finalize the discretization using a new method to the class. This step is required before the model can be labeled. +Here, we add data to the model and finalize the discretization using a new method to +the class. This step is required before the model can be labeled. .. literalinclude:: /../../pyomo/contrib/doe/examples/reactor_experiment.py :start-after: End equation definition @@ -256,7 +266,8 @@ Step 5: Exploratory analysis (Enumeration) After creating the subclass of the ``Experiment`` class, exploratory analysis is suggested to enumerate the design space to check if the problem is identifiable, -i.e., ensure that D-, E-optimality metrics are not small numbers near zero, and Modified E-optimality is not a big number. +i.e., ensure that D-, E-optimality metrics are not small numbers near zero, and +Modified E-optimality is not a big number. Additionally, it helps to initialize the model for the optimal experimental design step. Pyomo.DoE can perform exploratory sensitivity analysis with the ``compute_FIM_full_factorial`` method. @@ -318,16 +329,16 @@ most informative region is around :math:`C_{A0}=5.0` M, :math:`T=500.0` K with a :math:`\log_{10}` determinant of FIM being around 19, while the least informative region is around :math:`C_{A0}=1.0` M, :math:`T=300.0` K, with a :math:`\log_{10}` determinant of FIM being around -5. For D-, Pseudo A-, and -E-optimality we want to maximize the objective values, while for A- and Modified -E-optimality we want to minimize the objective values. +E-optimality we want to maximize the objective function, while for A- and Modified +E-optimality we want to minimize the objective function. Step 6: Performing an optimal experimental design ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ In Step 5, we defined the ``run_reactor_doe`` function. This function constructs -the DoE object and performs the exploratory sensitivity analysis. By default, -it also proceeds immediately to the optimal experimental design step +the DoE object and performs the exploratory sensitivity analysis. The way the function +is defined, it also proceeds immediately to the optimal experimental design step (applying ``run_doe`` on the ``DesignOfExperiments`` object). We can initialize the model with the result we obtained from the exploratory analysis (optimal point from the heatmaps) to help the optimal design step to speed From 52959713749224b040aab35330839753dac8c872 Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Fri, 6 Feb 2026 16:34:51 -0500 Subject: [PATCH 11/21] Add `Sphinx` label for Pyomo.DAE and Pyomo.DoE --- doc/OnlineDocs/explanation/analysis/doe/doe.rst | 2 ++ doc/OnlineDocs/explanation/modeling/dae.rst | 2 ++ 2 files changed, 4 insertions(+) diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index eb952b7aecb..9b610b399e0 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -1,3 +1,5 @@ +.. _pyomo.doe: + Pyomo.DoE ========= **Pyomo.DoE** (Pyomo Design of Experiments) is a Python library for model-based design diff --git a/doc/OnlineDocs/explanation/modeling/dae.rst b/doc/OnlineDocs/explanation/modeling/dae.rst index ac43ed35005..130813d61ff 100644 --- a/doc/OnlineDocs/explanation/modeling/dae.rst +++ b/doc/OnlineDocs/explanation/modeling/dae.rst @@ -1,3 +1,5 @@ +.. _pyomo.dae: + Dynamic Optimization with pyomo.DAE =================================== From 3bb025a21af82e6994f2839dc0631162fec8d048 Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Fri, 6 Feb 2026 16:42:30 -0500 Subject: [PATCH 12/21] Add the workshop flowchart --- .../explanation/analysis/doe/doe.rst | 5 +++-- .../explanation/analysis/doe/flowchart.png | Bin 160954 -> 0 bytes .../analysis/doe/pyomo_workflow_new.png | Bin 0 -> 167953 bytes 3 files changed, 3 insertions(+), 2 deletions(-) delete mode 100644 doc/OnlineDocs/explanation/analysis/doe/flowchart.png create mode 100644 doc/OnlineDocs/explanation/analysis/doe/pyomo_workflow_new.png diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index 9b610b399e0..8c73f723e26 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -29,10 +29,11 @@ gain from experiments by directly using science-based models with physically mea parameters. It is one key component in the model calibration and uncertainty quantification workflow shown below: -.. figure:: flowchart.png +.. figure:: pyomo_doe_workflow.png + :align: center :scale: 25 % - The exploratory analysis, parameter estimation, uncertainty analysis, and MBDoE are + The parameter estimation, uncertainty analysis, and MBDoE are combined into an iterative framework to select, refine, and calibrate science-based mathematical models with quantified uncertainty. 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zPLB9Rf%9Kia%{$M2v=0J&|X;&UhDB^#VF)qIEaA1sHRlOOaQ5%jrd32vzAJ&E0mRKFF$qTf~xqMSLp|6uPl{`D=sZ*r8e_Lai#oWI^W&213HzA z@GrGWh?#Utf?nZk^81CvXs^r)sNh8(1sQVV zKiS=@iuz~=bgDSkqiT9r*8E~{(~qxfXM06GhWVd|By!^gxRPo5)vy_HqOu6$dw}Slah#aP@R&-><)O(`+MLi-|YHH_3gWLYi(FI?}7FI%4k-m(cyKnD& zK|9(3omwF$H(-SqZVllQDIiUD`BD@aN2$UE0$Pq}ioCyR@f5|5Qjp zkec1Kr}v=QU3+%drdb)&>Bj7?J++Cqg3xSlKnH=`jcY@%ft+ z10IsY0pAifA%o+|=(8D4bS<1IaioubjJ#7kI@y;dn||jk1@trDE&fB)KPj4rMDo9a z_*A17YPMgrVroT@Ecqx&?~`A&k@Vhif=KQ4@94(kQ*)o((tflvc-!(KZj&F5kcw4v&p6FXo!(!$h>MydG zEYfGdbW|h;b?Xg|&ZBNSs}DL3O$wTTUB&qIP7cj|PQ3uU=`K=_WH>QQU;N*Hs3H)L zn!w-sX{+gfE=l`H)Ah+KQtgc|+wyOIZTk1|VJ5cgjMt|5qpupMr3Yo7%-GGEsc1s+ zUV}IAd3@0k$?2{7-+q{B;{2QU=4gR8a1l(TahltmVLza~% Date: Wed, 11 Feb 2026 07:54:02 -0500 Subject: [PATCH 15/21] Add clarification and note on confidence ellipse --- doc/OnlineDocs/explanation/analysis/doe/doe.rst | 17 +++++++++++------ 1 file changed, 11 insertions(+), 6 deletions(-) diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index 110bc05cfc8..0ff9f9912e6 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -90,7 +90,6 @@ where: * Parameters and design variables should be defined as Pyomo ``Var`` components when building the model using the ``Experiment`` class so that users can use both ``Parmest`` and ``Pyomo.DoE`` seamlessly. - Based on the above notation, the form of the MBDoE problem addressed in Pyomo.DoE is shown below: .. math:: @@ -128,20 +127,26 @@ Pyomo.DoE provides five design criteria :math:`\Psi` to measure the information - Geometrical meaning * - A-optimality - :math:`\text{trace}({\mathbf{M}}^{-1})` - - Dimensions of the enclosing box of the confidence ellipse + - Dimensions of the enclosing box of the confidence ellipse (derived from the covariance matrix) * - Pseudo A-optimality - :math:`\text{trace}({\mathbf{M}})` - - Dimensions of the enclosing box of the inverse of the confidence ellipse + - Dimensions of the enclosing box of the confidence ellipse (derived from the Fisher Information Matrix) * - D-optimality - :math:`\text{det}({\mathbf{M}})` - - Volume of the confidence ellipse + - Volume of the confidence ellipse (derived from the Fisher Information Matrix) * - E-optimality - :math:`\text{min eig}({\mathbf{M}})` - - Size of the longest axis of the confidence ellipse + - Size of the longest axis of the confidence ellipse (derived from the Fisher Information Matrix) * - Modified E-optimality - :math:`\text{cond}({\mathbf{M}})` - - Ratio of the longest axis to the shortest axis of the confidence ellipse + - Ratio of the longest axis to the shortest axis of the confidence ellipse (derived from the Fisher Information Matrix) +.. note:: + A confidence ellipse is a geometric representation of the uncertainty in parameter + estimates. It is derived from the covariance matrix or the Fisher Information + Matrix (FIM), depending on the design criterion. The ellipse illustrates the + spread and correlation of parameter estimates, with its axes corresponding to + the eigenvalues and eigenvectors of the respective matrix. In order to solve problems of the above, Pyomo.DoE implements the 2-stage stochastic program. Please see Wang and Dowling (2022) for details. From 5a99b61fa41ff8bc8fd41a342b93cc978a655b70 Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Wed, 11 Feb 2026 09:17:11 -0500 Subject: [PATCH 16/21] Enlage the workflow --- doc/OnlineDocs/explanation/analysis/doe/doe.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index 0ff9f9912e6..b82e6efa073 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -31,7 +31,7 @@ quantification workflow shown below: .. figure:: pyomo_workflow_new.png :align: center - :scale: 25 % + :scale: 90 % The parameter estimation, uncertainty analysis, and MBDoE are combined into an iterative framework to select, refine, and calibrate science-based From b48fd32ea256c2de33268c526aa259806054a60d Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Tue, 17 Feb 2026 16:12:11 -0500 Subject: [PATCH 17/21] Add more arguments in `reactor_example.py` --- pyomo/contrib/doe/examples/reactor_example.py | 17 +++++++++++------ pyomo/contrib/doe/tests/test_doe_solve.py | 9 ++++++--- 2 files changed, 17 insertions(+), 9 deletions(-) diff --git a/pyomo/contrib/doe/examples/reactor_example.py b/pyomo/contrib/doe/examples/reactor_example.py index c40799183bf..c480d954686 100644 --- a/pyomo/contrib/doe/examples/reactor_example.py +++ b/pyomo/contrib/doe/examples/reactor_example.py @@ -19,7 +19,10 @@ # Example for sensitivity analysis on the reactor experiment # After sensitivity analysis is done, we perform optimal DoE def run_reactor_doe( - n_points_for_design=9, + n_points_for_C0: int = 9, + n_points_for_T0: int = 9, + C0_bounds_for_factorial: tuple = (1, 5), + T0_bounds_for_factorial: tuple = (300, 700), compute_FIM_full_factorial=True, plot_factorial_results=True, figure_file_name="example_reactor_compute_FIM", @@ -31,8 +34,10 @@ def run_reactor_doe( Parameters ---------- - n_points_for_design : int, optional - number of points to use for the design ranges, by default 9 + n_points_for_C0 : int, optional + number of points to use for the C0 design range, by default 9 + n_points_for_T0 : int, optional + number of points to use for the T0 design range, by default 9 compute_FIM_full_factorial : bool, optional whether to compute the full factorial design, by default True plot_factorial_results : bool, optional @@ -90,8 +95,8 @@ def run_reactor_doe( if compute_FIM_full_factorial: # Make design ranges to compute the full factorial design design_ranges = { - "CA[0]": [1, 5, n_points_for_design], - "T[0]": [300, 700, n_points_for_design], + "CA[0]": [*C0_bounds_for_factorial, n_points_for_C0], + "T[0]": [*T0_bounds_for_factorial, n_points_for_T0], } # Compute the full factorial design with the sequential FIM calculation @@ -155,4 +160,4 @@ def run_reactor_doe( if __name__ == "__main__": - run_reactor_doe() + run_reactor_doe(figure_file_name=None) diff --git a/pyomo/contrib/doe/tests/test_doe_solve.py b/pyomo/contrib/doe/tests/test_doe_solve.py index 80a77b5f012..9e31accf894 100644 --- a/pyomo/contrib/doe/tests/test_doe_solve.py +++ b/pyomo/contrib/doe/tests/test_doe_solve.py @@ -616,7 +616,8 @@ def test_doe_full_factorial(self): 923636.598578955, ] ff = run_reactor_doe( - n_points_for_design=2, + n_points_for_C0=2, + n_points_for_T0=2, compute_FIM_full_factorial=False, plot_factorial_results=False, run_optimal_doe=False, @@ -884,7 +885,8 @@ def cleanup_files(): # Run the reactor example run_reactor_doe( - n_points_for_design=1, + n_points_for_C0=1, + n_points_for_T0=1, compute_FIM_full_factorial=True, plot_factorial_results=True, figure_file_name=prefix_linear, @@ -902,7 +904,8 @@ def cleanup_files(): # Run the reactor example with log scale run_reactor_doe( - n_points_for_design=1, + n_points_for_C0=1, + n_points_for_T0=1, compute_FIM_full_factorial=True, plot_factorial_results=True, figure_file_name=prefix_log, From 5cde1a6dfeb77be4d29706e3695d20ea3a0a733f Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Fri, 20 Feb 2026 15:25:55 -0500 Subject: [PATCH 18/21] Add sudden jump in the sensitivity plot --- doc/OnlineDocs/explanation/analysis/doe/doe.rst | 17 +++++++++++++++++ 1 file changed, 17 insertions(+) diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index b82e6efa073..a3f889fd9ca 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -340,6 +340,23 @@ with a :math:`\log_{10}` determinant of FIM being around -5. For D-, Pseudo A-, E-optimality we want to maximize the objective function, while for A- and Modified E-optimality we want to minimize the objective function. +However, in this sensitivity analysis plot (heatmap), we only varied the initial +concentration and the initial temperature, while the temperature at other time points is fixed at 300 K. + +.. math:: + :nowrap: + + \[ + T(t) = \begin{cases} + T_0, & t \le 0.125 \\ + 300\ \text{K}, & t > 0.125 + \end{cases} + \] + +Since all the temperature is at 300K when :math:`t > 0.125`, the parameters +:math:`A_1, E1, A_2, E_2` are not sensitive to the design variables, which +results in a small determinant of the FIM and a large condition number of the FIM. + Step 6: Performing an optimal experimental design ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ From 7b3882d73f2dd4dbcecdc29cbe58791256ba3f08 Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Fri, 20 Feb 2026 16:46:11 -0500 Subject: [PATCH 19/21] Update isothermal explanation in `doe.rst` [skip ci] --- .../explanation/analysis/doe/doe.rst | 20 +++++++++++++++---- 1 file changed, 16 insertions(+), 4 deletions(-) diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index a3f889fd9ca..7351cce2450 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -341,7 +341,8 @@ E-optimality we want to maximize the objective function, while for A- and Modifi E-optimality we want to minimize the objective function. However, in this sensitivity analysis plot (heatmap), we only varied the initial -concentration and the initial temperature, while the temperature at other time points is fixed at 300 K. +concentration and the initial temperature, while the temperature at other time +points is fixed at 300 K. .. math:: :nowrap: @@ -353,9 +354,20 @@ concentration and the initial temperature, while the temperature at other time p \end{cases} \] -Since all the temperature is at 300K when :math:`t > 0.125`, the parameters -:math:`A_1, E1, A_2, E_2` are not sensitive to the design variables, which -results in a small determinant of the FIM and a large condition number of the FIM. +If :math:`T_0 = 300\ \text{K}`, the reaction is conducted under strictly isothermal +conditions. Because the temperature is constant, the sensitivities of the species +concentrations with respect to the Arrhenius parameters (:math:`A_i` and :math:`E_i`) +become linearly dependent. This high correlation means the effects of the +pre-exponential factor and the activation energy cannot be uniquely distinguished +from the measurements. Consequently, the Fisher Information Matrix (FIM) becomes +ill-conditioned, resulting in a near-zero determinant and a very large condition number. + +To break this correlation and make the parameters identifiable, introducing a time- +varying temperature profile (for example, a temperature step or a ramp) is required. +As shown in the heatmap, when the initial temperature :math:`T_0` differs from the +subsequent 300 K baseline, such a temperature change breaks the linear dependence, +yielding a well-conditioned FIM and identifiable parameters. + Step 6: Performing an optimal experimental design From bfa34dcc5f3998eb74380cbdf389fec63e47e5b4 Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Fri, 6 Mar 2026 16:20:56 -0500 Subject: [PATCH 20/21] Implement Alex's suggestion Fix formatting and clarify descriptions in doe.rst documentation --- .../explanation/analysis/doe/doe.rst | 39 +++++++++---------- 1 file changed, 19 insertions(+), 20 deletions(-) diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index 7351cce2450..6d7a35601b8 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -9,7 +9,7 @@ Pyomo.DoE was originally created by **Jialu Wang** and **Alexander W. Dowling** University of Notre Dame as part of the `Carbon Capture Simulation for Industry Impact (CCSI2) `_ project, funded through the U.S. Department Of Energy Office of Fossil Energy with -assistance from **John Siirola**, **Bethany Nicholson**, **Miranda Mundt**,and **Hailey Lynch**. +assistance from **John Siirola**, **Bethany Nicholson**, **Miranda Mundt**, and **Hailey Lynch**. Significant improvements and extensions were contributed by **Dan Laky**, and **Shuvashish Mondal** with funding from the `Process Optimization & Modeling for Minerals Sustainability (PrOMMiS) `_ project @@ -98,7 +98,7 @@ Based on the above notation, the form of the MBDoE problem addressed in Pyomo.Do \begin{equation} \begin{aligned} \underset{\boldsymbol{\varphi}}{\max} \quad & \Psi (\mathbf{M}(\boldsymbol{\hat{\theta}}, \boldsymbol{\varphi})) \\ - \text{s.t.} \quad & \mathbf{M}(\boldsymbol{\hat{\theta}}, \boldsymbol{\varphi}) = \sum_r^{N_r} \sum_{r'}^{N_r} \tilde{\sigma}_{(r,r')}\mathbf{Q}_r^\mathbf{T} \mathbf{Q}_{r'} + \mathbf{V}_{\boldsymbol{\theta}}(\boldsymbol{\hat{\theta}})^{-1} \\ + \text{s.t.} \quad & \mathbf{M}(\boldsymbol{\hat{\theta}}, \boldsymbol{\varphi}) = \sum_r^{N_r} \sum_{r'}^{N_r} \tilde{\sigma}_{(r,r')}\mathbf{Q}_r^\mathbf{T} \mathbf{Q}_{r'} + \mathbf{M}_0 \\ & \dot{\mathbf{x}}(t) = \mathbf{f}(\mathbf{x}(t), \mathbf{z}(t), \mathbf{y}(t), \mathbf{u}(t), \overline{\mathbf{w}}, \boldsymbol{\hat{\theta}}) \\ & \mathbf{g}(\mathbf{x}(t), \mathbf{z}(t), \mathbf{y}(t), \mathbf{u}(t), \overline{\mathbf{w}},\boldsymbol{\hat{\theta}})=\mathbf{0} \\ & \mathbf{y} =\mathbf{h}(\mathbf{x}(t), \mathbf{z}(t), \mathbf{u}(t), \overline{\mathbf{w}},\boldsymbol{\hat{\theta}}) \\ @@ -111,12 +111,15 @@ Based on the above notation, the form of the MBDoE problem addressed in Pyomo.Do where: * :math:`\boldsymbol{\varphi}` are design variables, which are manipulated to maximize the information content of experiments. It should consist of one or more of :math:`\mathbf{u}(t), \mathbf{y}^{\mathbf{0}}({t_0}),\overline{\mathbf{w}}`. With a proper model formulation, the timepoints for control or measurements :math:`\mathbf{t}` can also be degrees of freedom. -* :math:`\mathbf{M}` is the Fisher information matrix (FIM), estimated as the inverse of the covariance matrix of parameter estimates :math:`\boldsymbol{\hat{\theta}}`. A large FIM indicates more information contained in the experiment for parameter estimation. +* :math:`\mathbf{M}` is the Fisher information matrix (FIM), approximated as the inverse of the covariance matrix of parameter estimates :math:`\boldsymbol{\hat{\theta}}`. A large FIM indicates more information contained in the experiment for parameter estimation. * :math:`\mathbf{Q}` is the dynamic sensitivity matrix, containing the partial derivatives of :math:`\mathbf{y}` with respect to :math:`\boldsymbol{\theta}`. * :math:`\Psi` is the scalar design criteria to measure the information content in the FIM. -* :math:`\mathbf{V}_{\boldsymbol{\theta}}(\boldsymbol{\hat{\theta}})^{-1}` is the FIM of previous experiments. +* :math:`\mathbf{M}_0` is the sum of all the FIMs from previous experiments. -Pyomo.DoE provides five design criteria :math:`\Psi` to measure the information in the FIM: +Pyomo.DoE provides five design criteria :math:`\Psi` to measure the information in the FIM. +The covariance matrix of parameter estimates is approximated as the inverse of the FIM, +i.e., :math:`\mathbf{V} \approx \mathbf{M}^{-1}`. +We can use the FIM or the covariance matrix to define the design criteria. .. list-table:: Pyomo.DoE design criteria :header-rows: 1 @@ -126,27 +129,24 @@ Pyomo.DoE provides five design criteria :math:`\Psi` to measure the information - Computation - Geometrical meaning * - A-optimality - - :math:`\text{trace}({\mathbf{M}}^{-1})` - - Dimensions of the enclosing box of the confidence ellipse (derived from the covariance matrix) + - :math:`\text{trace}(\mathbf{V}) = \text{trace}(\mathbf{M}^{-1})` + - Minimizing this is equivalent to minimizing enclosing box of the confidence ellipse * - Pseudo A-optimality - - :math:`\text{trace}({\mathbf{M}})` - - Dimensions of the enclosing box of the confidence ellipse (derived from the Fisher Information Matrix) + - :math:`\text{trace}(\mathbf{M})` + - Maximizing this is equivalent to maximizing total information in principal directions of the FIM * - D-optimality - - :math:`\text{det}({\mathbf{M}})` - - Volume of the confidence ellipse (derived from the Fisher Information Matrix) + - :math:`\det(\mathbf{M}) = 1/\det(\mathbf{V})` + - Maximizing this is equivalent to minimizing confidence-ellipsoid volume * - E-optimality - - :math:`\text{min eig}({\mathbf{M}})` - - Size of the longest axis of the confidence ellipse (derived from the Fisher Information Matrix) + - :math:`\lambda_{\min}(\mathbf{M}) = 1/\lambda_{\max}(\mathbf{V})` + - Maximizing this is equivalent to minimizing the longest axis of the confidence ellipse * - Modified E-optimality - - :math:`\text{cond}({\mathbf{M}})` - - Ratio of the longest axis to the shortest axis of the confidence ellipse (derived from the Fisher Information Matrix) + - :math:`\text{cond}(\mathbf{M}) = \text{cond}(\mathbf{V})` + - Minimizing this is equivalent to minimizing the ratio of the longest axis to the shortest axis of the confidence ellipse .. note:: A confidence ellipse is a geometric representation of the uncertainty in parameter - estimates. It is derived from the covariance matrix or the Fisher Information - Matrix (FIM), depending on the design criterion. The ellipse illustrates the - spread and correlation of parameter estimates, with its axes corresponding to - the eigenvalues and eigenvectors of the respective matrix. + estimates. It is derived from the covariance matrix :math:`\mathbf{V}`. In order to solve problems of the above, Pyomo.DoE implements the 2-stage stochastic program. Please see Wang and Dowling (2022) for details. @@ -386,4 +386,3 @@ the optimal design is an initial concentration of 5.0 mol/L and an initial temperature of 494 K with all other temperatures being 300 K. The corresponding :math:`\log_{10}` determinant of the FIM is 19.32. - From 7c2fccf4f4b390cc0b6cb1dc3476e1e94245727f Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Fri, 6 Mar 2026 16:22:33 -0500 Subject: [PATCH 21/21] Clarify description of A-optimality in documentation --- doc/OnlineDocs/explanation/analysis/doe/doe.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index 6d7a35601b8..ebf12f8ecfa 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -133,7 +133,7 @@ We can use the FIM or the covariance matrix to define the design criteria. - Minimizing this is equivalent to minimizing enclosing box of the confidence ellipse * - Pseudo A-optimality - :math:`\text{trace}(\mathbf{M})` - - Maximizing this is equivalent to maximizing total information in principal directions of the FIM + - Maximizing this is equivalent to maximizing the dimensions of the enclosing box of the Fisher Information Matrix * - D-optimality - :math:`\det(\mathbf{M}) = 1/\det(\mathbf{V})` - Maximizing this is equivalent to minimizing confidence-ellipsoid volume

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zBz*xTI{gCZ=?Cu?dI0Ltkjk47-7ENxhMYDC5ZnDCtVFF{{S&q?JM4oywd0yHC;l@U znS~_I7fw#jg?b-9NTXNYdyLsD3fE z8t0e|oHL&vgv~;W0?$tEleNcTh?}Y@%k@62Zk6>Whfem+=!GxPqg*#~jV55;2UsdQ zg6ASJ2u&!g+FxvW2=!6|Fj%LAkQYB*TdHFYiarH~)})|b{ySs%z6jnH4kA-p5^7Kg zJ4_F3Zgcaus+IoU+(Z+eD`l87VEV(`if^1_D;6Esf3sXIXM^;x`$0VjUl_iBarCkB zBQmUU7!*>CDz3i|n6UqiJOCguBk&>5eO{uIu(UD>zw~=k{C^<{C5!X#@c>W*Tl#&C zejhk=7M+opXof`*mZX@5XY}IeBMm^{{kj^9_d;r*abv-^?(|-*+t=#`}8%2_n_`{j>;~%VmCn zBvM&3|6h2JIjHO6ui?lN#$Ec24MUl0GMKax~jIxDZl# P0eqD1tHM6W8U_3x_Jssr literal 0 HcmV?d00001 From 6169d9823dc839d925140655f6cfa00555ed6487 Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Tue, 10 Feb 2026 15:08:29 -0500 Subject: [PATCH 13/21] Apply suggestions from code review Co-authored-by: Bethany Nicholson --- doc/OnlineDocs/explanation/analysis/doe/doe.rst | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index 8c73f723e26..0ac5838f5a1 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -12,7 +12,7 @@ project, funded through the U.S. Department Of Energy Office of Fossil Energy wi assistance from **John Siirola**, **Bethany Nicholson**, **Miranda Mundt**,and **Hailey Lynch**. Significant improvements and extensions were contributed by **Dan Laky**, and **Shuvashish Mondal** with funding from the -`Process Optimization & Modeling for Minerals Sustainability (PrOMMiS) `_ +`Process Optimization & Modeling for Minerals Sustainability (PrOMMiS) `_ project and the `University of Notre Dame `_. If you use Pyomo.DoE, please cite: @@ -114,10 +114,10 @@ where: * :math:`\boldsymbol{\varphi}` are design variables, which are manipulated to maximize the information content of experiments. It should consist of one or more of :math:`\mathbf{u}(t), \mathbf{y}^{\mathbf{0}}({t_0}),\overline{\mathbf{w}}`. With a proper model formulation, the timepoints for control or measurements :math:`\mathbf{t}` can also be degrees of freedom. * :math:`\mathbf{M}` is the Fisher information matrix (FIM), estimated as the inverse of the covariance matrix of parameter estimates :math:`\boldsymbol{\hat{\theta}}`. A large FIM indicates more information contained in the experiment for parameter estimation. * :math:`\mathbf{Q}` is the dynamic sensitivity matrix, containing the partial derivatives of :math:`\mathbf{y}` with respect to :math:`\boldsymbol{\theta}`. -* :math:`\Psi` is the scalar design criteria to measure the information content in FIM. +* :math:`\Psi` is the scalar design criteria to measure the information content in the FIM. * :math:`\mathbf{V}_{\boldsymbol{\theta}}(\boldsymbol{\hat{\theta}})^{-1}` is the FIM of previous experiments. -Pyomo.DoE provides five design criteria :math:`\Psi` to measure the information in FIM: +Pyomo.DoE provides five design criteria :math:`\Psi` to measure the information in the FIM: .. list-table:: Pyomo.DoE design criteria :header-rows: 1 From fc6a52392aa33bef759ad7ac17e9c9cde2984904 Mon Sep 17 00:00:00 2001 From: Shuvashish Mondal Date: Tue, 10 Feb 2026 15:39:07 -0500 Subject: [PATCH 14/21] Delete unused images and fix image rendering issue. --- .../explanation/analysis/doe/doe.rst | 6 +++--- .../explanation/analysis/doe/grid-1.png | Bin 611702 -> 0 bytes .../explanation/analysis/doe/uml.png | Bin 199419 -> 0 bytes 3 files changed, 3 insertions(+), 3 deletions(-) delete mode 100644 doc/OnlineDocs/explanation/analysis/doe/grid-1.png delete mode 100644 doc/OnlineDocs/explanation/analysis/doe/uml.png diff --git a/doc/OnlineDocs/explanation/analysis/doe/doe.rst b/doc/OnlineDocs/explanation/analysis/doe/doe.rst index 0ac5838f5a1..110bc05cfc8 100644 --- a/doc/OnlineDocs/explanation/analysis/doe/doe.rst +++ b/doc/OnlineDocs/explanation/analysis/doe/doe.rst @@ -29,9 +29,9 @@ gain from experiments by directly using science-based models with physically mea parameters. It is one key component in the model calibration and uncertainty quantification workflow shown below: -.. figure:: pyomo_doe_workflow.png - :align: center - :scale: 25 % +.. figure:: pyomo_workflow_new.png + :align: center + :scale: 25 % The parameter estimation, uncertainty analysis, and MBDoE are combined into an iterative framework to select, refine, and calibrate science-based diff --git a/doc/OnlineDocs/explanation/analysis/doe/grid-1.png b/doc/OnlineDocs/explanation/analysis/doe/grid-1.png deleted file mode 100644 index 6c96bbab7e078574ccedccc976366dcdfc434192..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 611702 zcmb5V2Ut_Vwl*9fKSN?-*G1dV7gN^_W=;0 zU(CaMeB`;LCPw5$k&TbrGPUQ5=e_x5saN?r%egIyZzufttt~|`=nwea7i1w&mA}hY zQJEn|PxMxfutM3O`?u=jP8g4@-wQ-9Wcp4pnH?+5j`r1n!!l;GkY;k_nN*CiTxs}w z=9?*6&uXPE(Ie;Blq_DZ18XYbN7tzm4g0v3cl3|aG>Hwl{o;o6Z5ivLXM`7p_o)He zbU!*6Ug18`8K9z1i72}Vg4{j%?0CE1EoQG?f2F9T%J?Ik(uhLdJgrMBtcWHc?lv=h 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