Physics-Informed Acceleration and Frequency Enhancement of 3D Earthquake Simulations using Multiple-Input Neural Operators and Conditional Diffusion Models

Authors : Filippo Gatti, Fanny Lehmann, Hugo Gabrielidis, Niccolò Perrone, Stefania Fresca, Stéphane Vialle, Didier Clouteau.

Abstract: We present a unified deep learning strategy that addresses the core challenges of computationally expensive and spectrally limited physics-based earthquake simulations. Numerical models simulating large-scale earthquake scenarios suffer from restrictive computational demands and often lack the fidelity required to reproduce high-frequency components, which are crucial for earthquake-resistant structural design, often requiring frequencies above 5 Hz and up to 40 Hz. To overcome this incompatibility, we utilize the Multiple-Input Fourier Neural Operator (MIFNO) as a fast, physics-based surrogate model, constrained by generative diffusion models that either perform super-resolution or correct spectral inaccuracies.
The MIFNO acts as a fast earthquake simulator by approximating the 3D elastodynamics Green’s operator. We designed the MIFNO to efficiently process complex, structured 3D geological fields ($\boldsymbol{a}$) alongside vector inputs describing source characteristics ($\boldsymbol{x}_s, \boldsymbol{\theta}_s$), such as position and moment tensor angles. Trained on the HEMEWS-3D database of 3D elastodynamic simulations, the MIFNO provides accurate predictions of surface velocity wavefields, particularly excelling in phase accuracy, with 80% of predictions achieving an excellent phase Goodness-Of-Fit (GOF) score greater than 8, ensuring correct wave arrival times. Crucially, the MIFNO achieves a massive speed-up compared to traditional numerical solvers (e.g., yielding 6.4 s of ground motion in around 10ms with one GPU, versus 43 min for numerical simulations using 32 CPUs). However, like many neural networks, the MIFNO exhibits a spectral bias, challenging its ability to capture small-scale, high-frequency fluctuations derived from complex physical phenomena.
We leverage conditional diffusion models to augment the frequency content or correct the MIFNO's output. In one strategy, we developed a Diffusion Transformer (DiT1D) for super-resolution, synthesizing realistic broadband accelerograms (0-30 Hz resolution). The DiT1D is explicitly guided by the low-frequency part of the signal (0-1 Hz), which is derived from 3D elastodynamics simulations or low-pass filtered records, thereby ensuring the fulfillment of minimum observable physics. This diffusion architecture learns the low-to-high frequency mapping, resulting in time histories suitable for structural design.
In a further integrated approach, we employ a Denoising Diffusion Probabilistic Model (DDPM) to directly correct the spectral bias of the MIFNO output. The MIFNO prediction of the ground motion velocity signal serves as the conditioning input for the DDPM. By integrating the DDPM, we successfully mitigate the observed mid-frequency spectral falloff inherent in the MIFNO predictions. This combination (MIFNO + DDPM) enhances the realism of the synthetic seismograms, providing superior phase GOF scores (with the mean Phase GOF improving from 6.65 to 7.52) and reducing frequency biases across the 0-5 Hz range compared to the standalone MIFNO model. By using the fast MIFNO as a preconditioner, we preserve the speed advantages of neural operators while achieving higher accuracy, paving the way for efficient physics-based probabilistic seismic hazard assessment.

‼️ Le séminaire peut être suivi en ligne suivant le lien : https://univ-amu-fr.zoom.us/j/95011527683?pwd=bTeNvaaZY75buaa7bRL0pcucXSASm7.1

Le mardi 10 mars 2026 à 11h00 / Amphithéâtre François Canac, LMA

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