# Integrating Fourier Neural Operators with Diffusion Models to improve Spectral Representation of Synthetic Earthquake Ground Motion Response

arXiv: https://arxiv.org/abs/2504.00757 · HTML: https://mlsanity.com/paper/2504.00757/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 18 references that are in the map.
- First posted on arXiv 1 Apr 2025.

## Builds on (most cited first, 3 of 3)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Factorized Fourier Neural Operators](https://mlsanity.com/paper/2111.13802/) (2021)
- [Multiple-Input Fourier Neural Operator (MIFNO) for source-dependent 3D elastodynamics](https://mlsanity.com/paper/2404.10115/) (2024)

## Built on by (most cited first, 2 of 2)

- [DETNO: A Diffusion-Enhanced Transformer Neural Operator for Long-Term Traffic Forecasting](https://mlsanity.com/paper/2508.19389/) (2025)
- [Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations](https://mlsanity.com/paper/2606.03936/) (2026)

## Abstract (arXiv)

Nuclear reactor buildings must be designed to withstand the dynamic load induced by strong ground motion earthquakes. For this reason, their structural behavior must be assessed in multiple realistic ground shaking scenarios (e.g., the Maximum Credible Earthquake). However, earthquake catalogs and recorded seismograms may not always be available in the region of interest. Therefore, synthetic earthquake ground motion is progressively being employed, although with some due precautions: earthquake physics is sometimes not well enough understood to be accurately reproduced with numerical tools, and the underlying epistemic uncertainties lead to prohibitive computational costs related to model calibration. In this study, we propose an AI physics-based approach to generate synthetic ground motion, based on the combination of a neural operator that approximates the elastodynamics Green's operator in arbitrary source-geology setups, enhanced by a denoising diffusion probabilistic model. The diffusion model is trained to correct the ground motion time series generated by the neural operator. Our results show that such an approach promisingly enhances the realism of the generated synthetic seismograms, with frequency biases and Goodness-Of-Fit (GOF) scores being improved by the diffusion model. This indicates that the latter is capable to mitigate the mid-frequency spectral falloff observed in the time series generated by the neural operator. Our method showcases fast and cheap inference in different site and source conditions.