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Rheological Universal Differential Equations: scientific machine learning for modeling complex fluids

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# Rheological Universal Differential Equations

This repository contains the code used to produce all results in the preprint: [Scientific Machine Learning for Modeling and Simulating Complex Fluids](https://arxiv.org/abs/2210.04431).

## Compatibility

The scripts used to train and test RUDEs on shear rheometric data were developed using [Julia](https://julialang.org/downloads/) v1.8.3, with the following packages: Flux v0.13.9, Optimization v3.10.0, Optimisers v0.2.14, OptimizationOptimisers v0.1.1, SciMLSensitivity v7.11.1, DifferentialEquations v7.6.0, Zygote v0.6.51, Enzyme v0.10.12, PyPlot v2.11.0, OrdinaryDiffEq v6.35.1, DataInterpolations v3.10.1, BSON v0.3.6, and FFTW v1.5.0.

Computational fluid dynamics simulations were performed using [OpenFOAM](https://openfoam.org/download/archive/) v9, with the [rheoTool](https://github.com/fppimenta/rheoTool) v5.0 toolbox.

The scripts used to process experimental linear response data and to plot OpenFOAM simulation results were developed using [Python](https://www.python.org/downloads/) 3.8.5, with the following packages: NumPy 1.19.2, Matplotlib 3.3.2, SciPy 1.5.2, CSV 1.0, and pandas 1.1.3.

## Contents

### `giesekus`

- `rude.jl`: Julia script to generate synthetic shear stress LAOS data for the Giesekus model, train a RUDE using this data, and test the RUDE on shear and normal stress data in LAOS as well as shear stress data in shear startup
- `tbnn.bson`: pre-trained model weights for a RUDE trained using the `rude.jl` script
- `OpenFOAM`: directory containing the files needed to simulate a 4:1 contraction flow
	- `Giesekus`: directory containing the setup files for an OpenFOAM simulation of the Giesekus model, including the mesh file (`system/blockMeshDict`), details for the integration and finite volume schemes (`system/fvSchemes` and `system/fvSolution`), definition of the constitutive model (`constant/constitutiveProperties`), and initial conditions (`0`)
	- `Oldroyd-BLog`: directory containing the setup files for an OpenFOAM simulation of the Oldroyd-B model (defined by the log-conformation tensor). Same file structure as the `Giesekus` directory
	- `RUDE`: directory containing the setup files for an OpenFOAM simulation of a trained RUDE. Same file structure as the `Giesekus` directory, with three additional files (`weights1.txt`, `weights2.txt`, and `weights3.txt`) containing the pre-trained weights for the TBNN layers obtained using the `rude.jl` script
	- `simdata`: directory containing selected results from the OpenFOAM simulations, including centerline velocities, velocity profiles, the velocity field, and streamlines
	- `make_plots.py`: Python script for plotting the simulation results contained in `simdata`

### `gel`

- `data`: directory containing experimental data for the metal-crosslinked polymer hydrogel. Includes the raw data output by TRIOS (`raw`) and pre-processed CSV files for LAOS and SAOS tests
- `fitlr.py`: Python script to fit the linear response of the gel to a single-mode Maxwell model
- `rude.jl`: Julia script to train a RUDE using the LAOS data, and predict the shear and normal stress response in another LAOS experiment (as well as an amplitude-sweep in LAOS)
- `weights_201.bson`: partially pre-trained model, terminated after an epoch of 200 training iterations on the lowest-amplitude LAOS experiment
- `weights_402.bson`: partially pre-trained model, terminated after an epoch of 200 training iterations on the two lowest-amplitude LAOS experiments, with training initialized using the `weights_201.bson` network
- `weights_603.bson`: fully pre-trained model, terminated after an epoch of 200 training iterations on all three training LAOS curves, with training initialized using the `weights_402.bson` network

## Contibuting

Inquiries and suggestions can be directed to krlennon[at]mit.edu.

## License

[GNU General Public License v3.0](https://choosealicense.com/licenses/gpl-3.0/)

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