Deep learning based surrogate models of physical systems have reached impressive fidelity in recent years, mostly due to high quality training data. However, they still lack the flexibility of traditional numerical solvers, for instance to accommodate non-cartesian domains. This project focuses on earthquake modelling in realistic 3D settings. Neural Operators were shown to be accurate surrogate models for 3D seismic wave propagation in propagation domains with a flat surface. [1, 2]. In parallel, several Neural Operator architectures have been proposed to handle irregular grids (e.g., GAOT [3]) but they have never been applied to earthquake data. In this project, we extend geometry-aware Neural Operators to 3D earthquake propagation with various topography. This will allow refined estimation of seismic hazard in regions with complex topography (basins, hills, peaks).
Internship main tasks
The tasks involve:
- defining realistic parametrizations of the Earth surface
- running numerical seismic wave simulations in 3D domains with chosen topography, using the HPC code SEM3D, to create a large dataset
- adapting Neural Operators to the non-cartesian 3D grids (e.g., GAOT) and train the model on the generated dataset
Requirements
We welcome students with the following background and skills. Also consider applying if you
do not fulfill all conditions.
- Master student in Computer Science, Data Science, HPC, or related field
- Familiarity with cluster computing (parallel computing, slurm)
- Proficient with python and pytorch
- Interest for physical problems
References
[1] Fanny Lehmann, Filippo Gatti, Micha¨el Bertin, and Didier Clouteau. 3D elastic wave propagation with a Factorized Fourier Neural Operator (F-FNO). Computer Methods in Applied Mechanics and Engineering, 420:116718, February 2024.
[2] Fanny Lehmann, Filippo Gatti, and Didier Clouteau. Multiple-input Fourier Neural Operator (MIFNO) for source-dependent 3D elastodynamics. Journal of Computational Physics, 527:113813, April 2025.
[3] Shizheng Wen, Arsh Kumbhat, Levi Lingsch, Sepehr Mousavi, Yizhou Zhao, Praveen Chandrashekar, and Siddhartha Mishra. Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains, May 2025.
