MIFNO

Train a Multiple-Input Fourier Neural Operator (MIFNO) to predict the solution of 3D source-dependent Partial Differential Equations (PDEs). The MIFNO is described in the article Multiple-Input Fourier Neural Operator (MIFNO) for source-dependent 3D elastodynamics. It extends the 3D Factorized Fourier Neural Operator (F-FNO) to PDEs with a source term. As such, the MIFNO contains a dedicated source branch that takes as input a vector of source parameters.

Data

The MIFNO is trained on the HEMEW^S-3D database that contains 30,000 simulations of the 3D elastic wave equation in heterogeneous media with different sources. The folder HEMEWS3D_S32_Z32_T320_fmax5_rot0_test contains 20 test samples that have already been preprocessed and are readily usable for machine learning tasks. To get the entire train dataset, you need to download the data from the HEMEW^S-3D repository and follow the preprocessing pipeline.

Training and Evaluation

The Github repository contains all the code to train and evaluate the MIFNO. A model checkpoint obtained after 300 epochs is provided in this repository.

Visualization

You can use the Jupyter notebook in this repository to run inference predictions with the MIFNO and plot ground motion predictions.

References

If you use this code, please cite

@article{lehmannMultipleinputFourierNeural2025,
  title = {Multiple-Input {{Fourier Neural Operator}} ({{MIFNO}}) for Source-Dependent {{3D}} Elastodynamics},
  author = {Lehmann, Fanny and Gatti, Filippo and Clouteau, Didier},
  year = {2025},
  journal = {Journal of Computational Physics},
  volume = {527},
  pages = {113813},
  issn = {00219991},
  doi = {10.1016/j.jcp.2025.113813},
}

If you use the HEMEW^S-3D database, please cite

@misc{lehmannPhysicsbasedSimulations3D2023a,
  title = {Physics-Based {{Simulations}} of {{3D Wave Propagation}} with {{Source Variability}}: \${{HEMEW}}{\textasciicircum}{{S-3D}}\$},
  shorttitle = {Physics-Based {{Simulations}} of {{3D Wave Propagation}} with {{Source Variability}}},
  author = {Lehmann, Fanny},
  year = {2023},
  publisher = {[object Object]},
  doi = {10.57745/LAI6YU},
  url = {https://doi.org/10.57745/LAI6YU}
}

and

@article{lehmannSyntheticGroundMotions2024,
  title = {Synthetic Ground Motions in Heterogeneous Geologies from Various Sources: The {{HEMEW}}{\textbackslash}textsuperscript\{\vphantom\}{{S}}\vphantom\{\}-{{3D}} Database},
  author = {Lehmann, F. and Gatti, F. and Bertin, M. and Clouteau, D.},
  year = {2024},
  journal = {Earth System Science Data},
  volume = {16},
  number = {9},
  pages = {3949--3972},
  doi = {10.5194/essd-16-3949-2024},
  url = {https://essd.copernicus.org/articles/16/3949/2024/}
}