bio-pinn

Physics-Informed Neural Network to predict the reaction rates of a BIOdiesel process

Physics-informed Neural Network

Physics-informed Neural Network (or PINN for short) is a deep learning algorithm that solves differential equations (ODEs or PDEs). In this work, we aim to use PINN for the purpose of identifying a chemical reaction. The mass of chemical species is conserved throughout the reaction. The accumulation rate of a specie depends on the rate at which it is consumed.

$\frac{d C_A}{dt} = - r_A$

with $C_A$ the concentration of reagant A, $t$ the idependant variable (the time), and $r_A$ the consumption rate.

The rate $r_A$ depends on a kinetic constant $k$ and a reaction order $\alpha$ that are a priori unknown, such as:

$r_A = k C_A^{\alpha}$

The PINN is able to perform a regression on data in order to solve de solution $C_A(t)$ and to identify the unknown kinetic parameters.

🧪 Biodiesel data (pinn > biodiesel_data)

The chemical reaction at study is the transesterification reaction in a microwave reactor where the glycerides in canola oil produce glycerol and biodiesel. First, the concentration data of glycerides are obtained via gas chromatography (GC-FID). The temperature is also measured within the reactor with an infrared sensor. Second, we build the architecture of the PINN. All the Python scripts are available in the biodiesel_data.

If you run the get_results.py script, you will automatically get the final predictions of the PINN. This script calls numerical.py in order to compare the PINN's predictions to a numerical solver.

In the pinn folder, we have the database and the scripts needed to train the PINN. Within this folder, 2 subfolders are present:

1. data: contains all the concentration data (from GC-FID) and the temperature data (from the infrared sensor).
2. results: contains all the predictions using the PINN and the numerical solver.

Within the same folder, we have the following scripts:

1. data.py: this script gathers the experimental data and creates the input tensor and the output tensor.
2. pinn.py: this script builds the architecture of the PINN. It uses the PyTorch library to do so.

• The class PINeuralNet (that uses the base class torch.nn.Module) allows to build the architecture, set up the parameters and defined the forward pass.
• The class Curiosity (named after the rover Curiosity from NASA that went on planet Mars to discover some wonders) trains the PINN model. The loss function is define in this class.

Generates loss.txt to store the final evaluation of the loss function and model.pt to keep the PINN model in memory.

3. main.py: calls the two scripts presented above to train the PINN. It adapts the learning rate and the regularization parameters to optimize the training and the predictions.

4. launch.sh: allows to send requests to computer clusters in order to use their GPU ressources for longer training.

🦾 Artificial data (pinn > artificial_data)

The folder alongside the biodiesel_data one is the artificial_data folder. Using noisy artificial data from a simplified reaction, we verify the implementation of the PINN implemented for the biodiesel process. The reaction is:

$A \leftrightarrow C + B$ and

$C \leftrightarrow D$

In this folder, we have 3 Python scripts: pinn.py builds the PINN, main.py trains the PINN and ode.py solves numericaly the ODEs of species molar balance.

Curve fit

Alongside the PINN algorithm, we implemented another non linear regressor for the purpose of comparing the performance of the PINN (a deep learning tool) with a more "classical" approach. The library SciPy offers a function called curve_fit. Using the Trust Region algorithm (or trf), we try to identify the same kinetic parameters. The curves that the regressor tries to fit are the species concentration over time solved by a numerical integrator, which is a Runge-Kutta method.