NODE for NIROM

Using a Tensorflow-based implementation of Neural ODEs (NODE) to develop non-intrusive reduced order models for CFD problems. Numerical comparisons are made with non-intrusive reduced order models (NIROM) that use Dynamic Mode Decomposition (DMD) as well as a combination of linear dimension reduction using Proper Orthogonal Decomposition (POD) and latent-space evolution using Radial Basis Function (RBF) interpolation.

For details please refer to -

S. Dutta, P. Rivera-casillas, and M. W. Farthing, “Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics,” in Proceedings of the AAAI 2021 Spring Symposium on Combining Artificial Intelligence and Machine Learning with Physical Sciences, 2021. Proceedings
arXiv

Getting Started

Dependencies

Python 3.x
Tensorflow TF 2 / 1.15.0 or above. Prefereably TF 2.0+, as the entire tfdiffeq codebase requires Eager Execution. Install either the CPU or the GPU version depending on available resources.
tfdiffeq - Installation directions are available at tfdiffeq.

A list of all the package requirements along with version information is provided in the requirements file.

Executing program

NODE scripts, available inside the notebooks directory, can be invoked with various user-specified configuration options to test different NN models.
DMD and PODRBF notebooks are also available inside the notebooks directory.
High-fidelity snapshot data files are available for

Shallow Water models - Link,

Navier Stokes model - Link.

These data files should be placed in the directory.

Some pre-trained ROM model files are available at NIROM models. The DMD and PODRBF trained models should be placed in the directory, and the NODE models should be placed inside the corresponding subdirectory of .

Authors

Sourav Dutta - Sourav.Dutta@erdc.dren.mil - ERDC-CHL
Matthew Farthing - Matthew.W.Farthing@erdc.dren.mil - ERDC-CHL
Peter Rivera-Casillas - Peter.G.Rivera-Casillas@erdc.dren.mil - ERDC-ITL

License

This project is licensed under the MIT License - see the LICENSE file for details

Reference

If you found this library useful in your research, please consider citing

@inproceedings{dutta2021aaai,
title={Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics},
author={Dutta, Sourav and Rivera-Casillas, Peter and Farthing, Matthew W.},
booktitle={Proceedings of the AAAI 2021 Spring Symposium on Combining Artificial Intelligence and Machine Learning with Physical Sciences},
url={https://sites.google.com/view/aaai-mlps/proceedings?authuser=0},
year={2021},
publisher={CEUR-WS},
address={Stanford, CA, USA, March 22nd to 24th, 2021},
}

Acknowledgments

Thank you to ERDC-HPC facilities for support with valuable computational infrastructure
Thank you to ORISE for support with appointment to the Postgraduate Research Participation Program.

Inspiration, code snippets, etc.