# Broadband Ground Motion Synthesis via Generative Adversarial Neural Operators: Development and Validation

arXiv: https://arxiv.org/abs/2309.03447 · HTML: https://mlsanity.com/paper/2309.03447/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 69 references that are in the map.
- First posted on arXiv 7 Sep 2023.

## Builds on (most cited first, 13 of 13)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [StyleFlow: Attribute-conditioned Exploration of StyleGAN-Generated Images using Conditional Continuous Normalizing Flows](https://mlsanity.com/paper/2008.02401/) (2020)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [U-NO: U-shaped Neural Operators](https://mlsanity.com/paper/2204.11127/) (2022)
- [Generative Adversarial Neural Operators](https://mlsanity.com/paper/2205.03017/) (2022)
- [Seismic wave propagation and inversion with Neural Operators](https://mlsanity.com/paper/2108.05421/) (2021)
- [Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Model](https://mlsanity.com/paper/1909.04711/) (2019)
- [Faces `a la Carte: Text-to-Face Generation via Attribute Disentanglement](https://mlsanity.com/paper/2006.07606/) (2020)

## Built on by (most cited first, 12 of 12)

- [Neural Operators for Accelerating Scientific Simulations and Design](https://mlsanity.com/paper/2309.15325/) (2023)
- [Neural Operators with Localized Integral and Differential Kernels](https://mlsanity.com/paper/2402.16845/) (2024)
- [Guided Diffusion Sampling on Function Spaces with Applications to PDEs](https://mlsanity.com/paper/2505.17004/) (2025)
- [Stochastic Process Learning via Operator Flow Matching](https://mlsanity.com/paper/2501.04126/) (2025)
- [Mesh-Informed Neural Operator : A Transformer Generative Approach](https://mlsanity.com/paper/2506.16656/) (2025)
- [Universal Functional Regression with Neural Operator Flows](https://mlsanity.com/paper/2404.02986/) (2024)
- [Learning Physics for Unveiling Hidden Earthquake Ground Motions via Conditional Generative Modeling](https://mlsanity.com/paper/2407.15089/) (2024)
- [High Resolution Seismic Waveform Generation using Denoising Diffusion](https://mlsanity.com/paper/2410.19343/) (2024)
- [Broadband Ground Motion Synthesis by Diffusion Model with Minimal Condition](https://mlsanity.com/paper/2412.17333/) (2024)
- [Neural Spline Operators for Risk Quantification in Stochastic Systems](https://mlsanity.com/paper/2508.20288/) (2025)
- [TimesNet-Gen: Deep Learning-based Site Specific Strong Motion Generation](https://mlsanity.com/paper/2512.04694/) (2025)
- [From Complex Dynamics to DynFormer: Rethinking Transformers for PDEs](https://mlsanity.com/paper/2603.03112/) (2026)

## Abstract (arXiv)

We present a data-driven framework for ground-motion synthesis that generates three-component acceleration time histories conditioned on moment magnitude, rupture distance , time-average shear-wave velocity at the top 30m (VS30), and style of faulting. We use a Generative Adversarial Neural Operator (GANO), a resolution invariant architecture that guarantees model training independent of the data sampling frequency. We first present the conditional ground-motion synthesis algorithm (cGM-GANO) and discuss its advantages compared to previous work. We next train cGM-GANO on simulated ground motions generated by the Southern California Earthquake Center Broadband Platform (BBP) and on recorded KiK-net data and show that the model can learn the overall magnitude, distance, and VS30 scaling of effective amplitude spectra (EAS) ordinates and pseudo-spectral accelerations (PSA). Results specifically show that cGM-GANO produces consistent median scaling with the training data for the corresponding tectonic environments over a wide range of frequencies for scenarios with sufficient data coverage. For the BBP dataset, cGM-GANO cannot learn the ground motion scaling of the stochastic frequency components; for the KiK-net dataset, the largest misfit is observed at short distances and for soft soil conditions due to the scarcity of such data. Except for these conditions, the aleatory variability of EAS and PSA are captured reasonably well. Lastly, cGM-GANO produces similar median scaling to traditional GMMs for frequencies greater than 1Hz for both PSA and EAS but underestimates the aleatory variability of EAS. Discrepancies in the comparisons between the synthetic ground motions and GMMs are attributed to inconsistencies between the training dataset and the datasets used in GMM development. Our pilot study demonstrates GANO's potential for efficient synthesis of broad-band ground motions