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Machine learning methods (for fluid dynamics and dynamical systems)

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# Machine learning methods for fluid dynamics

CFD simulations are performed in OpenFOAMv2506 docker for convenience, and machine learning is performed using PyTorch and TensorFlow.

## py_foam_coupling
This folder includes files to run OpenFOAM simulations from python and organizes data to perform machine learning.
- coupling.py : Methods to execute OpenFOAM from Python.
- vtk_foam.py : Loads VTK files and reports from OpenFOAM directory and outputs a dictionary of the results as a pickle
- dataToML.py : Loads several dictionaries and organizes the results suitable to perform machine learning.

## mlp
Multi-Layer Perceptron (DNN) class to parametrically create and assess DNN models.
This is tested on a simple sine function, branin function and CFD data (organized in corresponding directories)

## smt_ml
Surrogate Models from smt library. Best suited for cases with MISO problems.
Uses RBF, Kriging and Polynomial models and creates a weighted average surrogate.
Includes LHS sampling for DOE and generates infill points based on either optima or max uncertainty from Kriging using Particle Swarm optimization. 
Tested on 1D, 2D and higher dimensional problems.

Based on: 
- A Python surrogate modeling framework with derivatives. Advances in Engineering Software, 2019.

- Miranda L.J., (2018). PySwarms: a research toolkit for Particle Swarm Optimization in Python. Journal of Open Source Software, 3(21), 433, https://doi.org/10.21105/joss.00433

- Goel, Tushar, Raphael T. Haftka, Wei Shyy, and Nestor V. Queipo. “Ensemble of Surrogates.” Structural and Multidisciplinary Optimization 33, no. 3 (2007): 199–216. https://doi.org/10.1007/s00158-006-0051-9.

## autoencoder
CNN autoencoder for fluid dynamics results on a structured grid. 
Can be operated as a vanilla AE, beta-VAE, total-correlation VAE (TCVAE) with/without ResNet-like skip connections. 
Tested on the two fluid datasets. A full DOE of hyper-parameter sensitivity study was performed and the energy of reconstruction and latent space disentanglement were recorded. Additionally, the latent space evolution in time is identified using Discrete SINDy (Sparse Identification of Non-linear Dynamics) using pysindy package.

Based on:
- Eivazi, Hamidreza, Soledad Le Clainche, Sergio Hoyas, and Ricardo Vinuesa. “Towards Extraction of Orthogonal and Parsimonious Non-Linear Modes from Turbulent Flows.” Expert Systems with Applications 202 (September 2022): 117038. https://doi.org/10.1016/j.eswa.2022.117038.

- Wang, Yuning, Alberto Solera-Rico, Carlos Sanmiguel Vila, and Ricardo Vinuesa. “Towards Optimal β -Variational Autoencoders Combined with Transformers for Reduced-Order Modelling of Turbulent Flows.” International Journal of Heat and Fluid Flow 105 (February 2024): 109254. https://doi.org/10.1016/j.ijheatfluidflow.2023.109254.

- Solera-Rico, Alberto, Carlos Sanmiguel Vila, Miguel Gómez-López, et al. “β-Variational Autoencoders and Transformers for Reduced-Order Modelling of Fluid Flows.” Nature Communications 15, no. 1 (2024): 1361. https://doi.org/10.1038/s41467-024-45578-4.

- Chen, Ricky T Q, Xuechen Li, Roger Grosse, and David Duvenaud. Isolating Sources of Disentanglement in VAEs. n.d.

# pinns
Physics Informed Neural Network on Tensorflow. MLP with physics-based loss functions evaluated on spatial points. Boundary and collocated points of channel flow and cavity are generated using generate_geometry.py. Laminar Navier-Stokes and 2D steady and transient heat equations are available in physics_models. Reinitialization loss for avoiding local optima (Lee 2025), hard constraint functions based on Sheikholeslami are implemented.

Based on:
- Eivazi, Hamidreza, Mojtaba Tahani, Philipp Schlatter, and Ricardo Vinuesa. “Physics-Informed Neural Networks for Solving Reynolds-Averaged Navier–Stokes Equations.” Physics of Fluids 34, no. 7 (2022): 075117. https://doi.org/10.1063/5.0095270.

- Lee, Jongmok, Seungmin Shin, Taewan Kim, et al. “Physics Informed Neural Networks for Fluid Flow Analysis with Repetitive Parameter Initialization.” Scientific Reports 15, no. 1 (2025): 16740. https://doi.org/10.1038/s41598-025-99354-5.

- Lu, Lu, Raphael Pestourie, Wenjie Yao, Zhicheng Wang, Francesc Verdugo, and Steven G. Johnson. “Physics-Informed Neural Networks with Hard Constraints for Inverse Design.” arXiv:2102.04626. Preprint, arXiv, February 9, 2021. https://doi.org/10.48550/arXiv.2102.04626.

- Sheikholeslami, Mohammad. "Physics-informed neural networks with hard and soft boundary conditions for problems in fluid dynamics." (2025).

## dmd
Perform dynamic mode decomposition (DMD) on fluid data to obtain future state prediction. Perform modal analysis, compare POD and DMD modes, and DMD mode frequencies. Includes dmd_jax for jax compiled dmd for ~10-100x faster computation of future states. 
Tested on the fluid datasets.

Based on:
- Brunton, Steven L., and J. Nathan Kutz. Data-driven science and engineering: Machine learning, dynamical systems, and control. Cambridge University Press, 2022.

## mpc_sindy
Perform Model Predictive Control of an arbitrary plant model with surrogate model estimated from SINDyC. The models are accelerated using JAX framework for potentially overcoming MPC bottlenecks in real-time control. JAX works only on Polynomial, Fourier and Concatenated library classes. 
Tested on analtical problems such as Lorenz, spring damper, pendulum and double integrator.

Based on:
- Fasel, Urban, Eurika Kaiser, J. Nathan Kutz, Bingni W. Brunton, and Steven L. Brunton. "Sindy with control: A tutorial." In 2021 60th IEEE conference on decision and control (CDC), pp. 16-21. IEEE, 2021.

- Kaiser, E., J. N. Kutz, and S. L. Brunton. “Sparse Identification of Nonlinear Dynamics for Model Predictive Control in the Low-Data Limit.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2219 (2018): 20180335. https://doi.org/10.1098/rspa.2018.0335.

- Kaptanoglu, Alan A., Brian M. de Silva, Urban Fasel, Kadierdan Kaheman, Andy J. Goldschmidt, Jared L. Callaham, Charles B. Delahunt et al. "PySINDy: A comprehensive Python package for robust sparse system identification." arXiv preprint arXiv:2111.08481 (2021).

## datasets
Tested on two CFD test cases: 
- Flow over two colinear plates with u and v velocities (plates_cfd), and 
- Flow over a cylinder at Re~1e4 with u, v velocity, turbulent kinetic energy and z-vorticity (cylinder_cfd).

## test_cases
Cases with complete workflow.
- airFoil_2D: Perform angle of attack simulations and create an MLP model for AoA to pressure, surface pressure and velocities. AoA vs Cd/Cl surrogates created using smt_ml. 
- ahmed_body: Perform drag optimization of ahmed body by modifying the real slant length and angle. Geometry created in Blender. smt_ml is used for design exploration and optimization, smt_data.func() in smt_data.py handles model creation, OpenFOAM workflow, and retrieves CdA from the results.

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