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.

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).

• 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
• ...

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

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. FMIFlux.jl currently only works with FMI2-FMUs. All shipped examples are automatically tested under Julia version v1 (latest) on Windows (latest).

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

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

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