This repository is a curated collection of tutorials that delve into various reduced-order modeling techniques. Utilizing Jupyter Notebooks as the instructional medium, these tutorials provide an interactive, hands-on approach to understanding complex computational models like DeepONet, FNO, POD-DL-ROM, and DL-ROM. Each notebook is designed to function as a standalone tutorial and includes provisions for automatic data retrieval, facilitating execution on both local machines and Google Colab environments.
To execute the tutorials, certain Python packages must be installed. This can be done by executing the following command:
pip install -r requirements.txtLi, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020). Fourier neural operator for parametric partial differential equations. arXiv preprint arXiv:2010.08895. Paper
Lu, L., Jin, P., & Karniadakis, G. E. (2019). Deeponet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators. arXiv preprint arXiv:1910.03193. Paper
Fresca, S., & Manzoni, A. (2022). POD-DL-ROM: Enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering, 388, 114181. Paper
Pant, P., Doshi, R., Bahl, P., & Barati Farimani, A. (2021). Deep learning for reduced order modelling and efficient temporal evolution of fluid simulations. Physics of Fluids, 33(10). Paper
In order to facilitate ease of navigation and comprehension, a standard naming schema has been adopted for the Jupyter notebooks:
[Model]_[Equation/Problem+Dimension]_[TAG].ipynb
- Model: Represents the computational model or algorithm under study (e.g., FNO, DLROM).
- Equation/Problem+Dimension: Specifies the mathematical problem or equation being solved along with its spatial dimensions (e.g., Burgers1D, NOAA2D).
- TAG: An optional identifier providing supplementary context or categorizing the notebook's difficulty level or specific focus (e.g., Intro, Advanced, DataPrep).
For users interested in a more interactive learning experience, Google Colab versions of these tutorials are available. Click the links below to open the Colab notebooks:
The datasets required for the tutorials are automatically fetched during runtime.
This repository is under the MIT License. Details can be found in the LICENSE file.