Large-Scale 3D Ground-Motion Synthesis with Physics-Inspired Latent Operator Flow Matching

Abstract

Earthquake hazard analysis and design of spatially distributed infrastructure, such as power grids and energy pipeline networks, require scenario-specific ground-motion time histories with realistic frequency content and spatiotemporal coherence. However, producing the large ensembles needed for uncertainty quantification with physics-based simulations is computationally intensive and impractical for engineering workflows. To address this challenge, we introduce Ground-Motion Flow (GMFlow), a physics-inspired latent operator flow matching framework that generates realistic, large-scale regional ground-motion time-histories conditioned on physical parameters. Validated on simulated earthquake scenarios in the San Francisco Bay Area, GMFlow generates spatially coherent ground motion across more than 9 million grid points in seconds, achieving a 10,000-fold speedup over the simulation workflow, which opens a path toward rapid and uncertainty-aware hazard assessment for distributed infrastructure. More broadly, GMFlow advances mesh-agnostic functional generative modeling and could potentially be extended to the synthesis of large-scale spatiotemporal physical fields in diverse scientific domains.

Figures (20)

• Figure 1: Workflow for physics-based ground-motion simulation in the San Francisco Bay Area.(left) A 3D representation of the heterogeneous geological structure beneath the Bay Area, adopted from https://www.usgs.gov/media/ images/3d-geologic-model with permission. (center) The problem (computational) domain used for the numerical simulations. (right) An example of finite-fault event simulation.
• Figure 2: GmFlow model architecture and two-stage synthesis pipeline.(top) The original surface wavefield $u$ is filtered and downsampled to a low-frequency representation $u_f$; the reverse mapping is performed by a super-resolution neural operator. (bottom) An encoder--decoder neural operator encodes $u_f$ to a latent code $z_1$, and decodes it back to $u_f$; conditional flow matching transports $z_0\!\sim\!\mathcal{N}(0,I)$ to $z_1$ given physical conditions $c$.
• Figure 3: Evaluation of GmFlow on a representative $M_w\,4.4$ point-source scenario.(A--B) Side-by-side comparison of the ground-truth velocity wavefield and a single stochastic realization generated by GmFlow at selected time steps (snapshots). Orange dash and solid lines represent Hayward fault and coastline, respectively. (C) Peak ground velocity (PGV; $m/s$), comparing the ground truth, one synthetic realization, the ensemble mean ($N=100$), and the predictive uncertainty. (D) Spatial maps of the Fourier amplitude spectrum (FAS) at 0.25 Hz (top) and 0.75 Hz (bottom). (E) Normalized cross-correlation (NCC) for spatiotemporal coherence analysis, showing the peak correlation coefficient (top) and the corresponding time lag (bottom). (F) Geographic map of the computational domain, with epicenter (purple star) and the virtual seismic profiles A1--A2 and B1--B2 indicated. (G--H) Time--distance plots along profiles A1--A2 and B1--B2.
• Figure 4: Evaluation of GmFlow on a representative $M_w\,7.0$ fintie-rupture scenario.
• Figure 5: Station-level spectral evaluation across magnitude range.(A, C, E) Spatial distribution of four randomly selected validation stations (triangles) and the epicenter (star) for $M_w$ 4.4, 6.0, and 7.0 scenarios. (B, D, F) Comparison of the horizontal (power-mean) and vertical Fourier Amplitude Spectra (FAS) for the ground truth (blue) and synthetic realizations (orange/red). The solid lines for the synthetics represent the geometric mean of $N=100$ realizations, while the shaded regions indicate the $\pm1$ geometric standard deviation.