FMIFlux.jl

What is FMIFlux.jl?

FMIFlux.jl is a free-to-use software library for the Julia programming language, which offers the ability to simply place your FMU (fmi-standard.org) everywhere inside of your ML topologies and still keep the resulting models trainable with a standard (or custom) FluxML training process. This includes for example:

• NeuralODEs including FMUs, so called Neural Functional Mock-up Units (NeuralFMUs): You can place FMUs inside of your ML topology.
• PINNs including FMUs, so called Functional Mock-Up Unit informed Neural Networks (FMUINNs): You can evaluate FMUs inside of your loss function.

How can I use FMIFlux.jl?

1. Open a Julia-REPL, switch to package mode using ], activate your preferred environment.

2. Install FMIFlux.jl:

(@v1) pkg> add FMIFlux

3. If you want to check that everything works correctly, you can run the tests bundled with FMIFlux.jl:

(@v1) pkg> test FMIFlux

4. Have a look inside the examples folder in the examples branch or the examples section of the documentation. All examples are available as Julia-Script (.jl), Jupyter-Notebook (.ipynb) and Markdown (.md).

What is currently supported in FMIFlux.jl?

• building and training ME-NeuralFMUs (NeuralODEs) with support for event-handling (DiffEqCallbacks.jl) and discontinuous sensitivity analysis (SciMLSensitivity.jl)
• building and training CS-NeuralFMUs
• building and training NeuralFMUs consisiting of multiple FMUs
• building and training FMUINNs (PINNs)
• different AD-frameworks: ForwardDiff.jl (CI-tested), ReverseDiff.jl (CI-tested, default setting), FiniteDiff.jl (not CI-tested) and Zygote.jl (not CI-tested)
• use Flux.jl optimisers as well as the ones from Optim.jl
• using the entire DifferentialEquations.jl solver suite (autodiff=false for implicit solvers)
• ...

(Current) Limitations

• Sensitivity information over state change by event $\partial x^{+} / \partial x^{-}$ can't be accessed in FMI. These sensitivities are simplified on basis of one of the following assumptions (defined by user): (1) the state after event depends on nothing, so sensitivities are zero or (2) the state after event instance only depends on the same state before the event instance The second is often correct for e.g. mechanical contacts, but may lead to wrong gradients for arbitrary discontinuous systems. However even if the gradient might not be 100% correct in any case, gradients are often usable for optimization tasks. This issue is also part of the OpenScaling research project.

• Discontinuous systems with implicite solvers use continuous adjoints instead of automatic differentiation through the ODE solver. This might lead to issues, because FMUs are by design not simulatable backward in time. On the other hand, many FMUs are capabale of doing so. This issue is also part of the OpenScaling research project.

• Implicit solvers using autodiff=true is not supported (now), but you can use implicit solvers with autodiff=false.

• For now, only FMI version 2.0 is supported, but FMI 3.0 support is coming with the OpenScaling research project.

What is under development in FMIFlux.jl?

• performance optimizations
• multi threaded CPU training
• improved documentation
• more examples
• FMI3 integration
• ...

What Platforms are supported?

FMIFlux.jl is tested (and testing) under Julia versions v1.6 (LTS) and v1 (latest) on Windows (latest) and Ubuntu (latest). MacOS should work, but untested. All shipped examples are automatically tested under Julia version v1 (latest) on Windows (latest).

What FMI.jl-Library should I use?

To keep dependencies nice and clean, the original package FMI.jl had been split into new packages:

• FMI.jl: High level loading, manipulating, saving or building entire FMUs from scratch
• FMIImport.jl: Importing FMUs into Julia
• FMIExport.jl: Exporting stand-alone FMUs from Julia Code
• FMICore.jl: C-code wrapper for the FMI-standard
• FMISensitivity.jl: Static and dynamic sensitivities over FMUs
• FMIBuild.jl: Compiler/Compilation dependencies for FMIExport.jl
• FMIFlux.jl: Machine Learning with FMUs (differentiation over FMUs)
• FMIZoo.jl: A collection of testing and example FMUs

How to cite?

Tobias Thummerer, Johannes Stoljar and Lars Mikelsons. 2022. NeuralFMU: presenting a workflow for integrating hybrid NeuralODEs into real-world applications. Electronics 11, 19, 3202. DOI: 10.3390/electronics11193202

Tobias Thummerer, Lars Mikelsons and Josef Kircher. 2021. NeuralFMU: towards structural integration of FMUs into neural networks. Martin Sjölund, Lena Buffoni, Adrian Pop and Lennart Ochel (Ed.). Proceedings of 14th Modelica Conference 2021, Linköping, Sweden, September 20-24, 2021. Linköping University Electronic Press, Linköping (Linköping Electronic Conference Proceedings ; 181), 297-306. DOI: 10.3384/ecp21181297

Related publications?

Tobias Thummerer, Johannes Tintenherr, Lars Mikelsons 2021. Hybrid modeling of the human cardiovascular system using NeuralFMUs Journal of Physics: Conference Series 2090, 1, 012155. DOI: 10.1088/1742-6596/2090/1/012155