arXiv subjects

Caifeng Zou

Publications and source records attributed to Caifeng Zou.

7 recordsLinked to original sources

arXiv2026

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

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.

cs.LG↗

arXiv2026

Enforcing Reciprocity in Operator Learning for Seismic Wave Propagation

Accurate and efficient wavefield modeling underpins seismic structure and source studies. Traditional methods comply with physical laws but are computationally intensive. Data-driven methods, while opening new avenues for advancement, have yet to incorporate strict physical consistency. The principle of reciprocity is one of the most fundamental physical laws in wave propagation. We introduce the Reciprocity-Enforced Neural Operator (RENO), a transformer-based architecture for modeling seismic wave propagation that hard-codes the reciprocity principle. The model leverages the cross-attention mechanism and commutative operations to guarantee invariance under swapping source and receiver positions. Beyond improved physical consistency, the proposed architecture supports simultaneous realizations for multiple sources. This yields an order-of-magnitude inference speedup at a similar memory footprint over a conventional neural operator on a realistic multi-source configuration. We demonstrate the functionality using the reciprocity relation for particle velocity fields under single forces. This architecture is also applicable to pressure fields under dilatational sources and travel-time fields governed by the eikonal equation, paving the way for encoding more complex reciprocity relations.

physics.geo-ph↗

arXiv2025

Ambient Noise Full Waveform Inversion with Neural Operators

Numerical simulations of seismic wave propagation are crucial for investigating velocity structures and improving seismic hazard assessment. However, standard methods such as finite difference or finite element are computationally expensive. Recent studies have shown that a new class of machine learning models, called neural operators, can solve the elastodynamic wave equation orders of magnitude faster than conventional methods. Full waveform inversion is a prime beneficiary of the accelerated simulations. Neural operators, as end-to-end differentiable operators, combined with automatic differentiation, provide an alternative approach to the adjoint-state method. State-of-the-art optimization techniques built into PyTorch provide neural operators with greater flexibility to improve the optimization dynamics of full waveform inversion, thereby mitigating cycle-skipping problems. In this study, we demonstrate the first application of neural operators for full waveform inversion on a real seismic dataset, which consists of several nodal transects collected across the San Gabriel, Chino, and San Bernardino basins in the Los Angeles metropolitan area.

physics.geo-ph↗

arXiv2025

InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences

Plug-and-play diffusion priors (PnPDP) have emerged as a promising research direction for solving inverse problems. However, current studies primarily focus on natural image restoration, leaving the performance of these algorithms in scientific inverse problems largely unexplored. To address this gap, we introduce \textsc{InverseBench}, a framework that evaluates diffusion models across five distinct scientific inverse problems. These problems present unique structural challenges that differ from existing benchmarks, arising from critical scientific applications such as optical tomography, medical imaging, black hole imaging, seismology, and fluid dynamics. With \textsc{InverseBench}, we benchmark 14 inverse problem algorithms that use plug-and-play diffusion priors against strong, domain-specific baselines, offering valuable new insights into the strengths and weaknesses of existing algorithms. To facilitate further research and development, we open-source the codebase, along with datasets and pre-trained models, at https://devzhk.github.io/InverseBench/.

cs.LG↗

arXiv2025

Reducing Frequency Bias of Fourier Neural Operators in 3D Seismic Wavefield Simulations Through Multi-Stage Training

The recent development of Neural Operator (NeurOp) learning for solutions to the elastic wave equation shows promising results and provides the basis for fast large-scale simulations for different seismological applications. In this paper, we use the Fourier Neural Operator (FNO) model to directly solve the 3D Helmholtz wave equation for fast seismic ground motion simulations on different frequencies, and show the frequency bias of the FNO model, i.e. it learns the lower frequencies better comparing to the higher frequencies. To reduce the frequency bias, we adopt the multi-stage FNO training, i.e., after training a 1st stage FNO model for estimating the ground motion, we use a second FNO model as the 2nd stage to learn from the residual, which greatly reduced the errors on the higher frequencies. By adopting this multi-stage training, the FNO models show reduced biases on higher frequencies, which enhanced the overall results of the ground motion simulations. Thus the multi-stage training FNO improves the accuracy and realism of the ground motion simulations.

physics.geo-ph↗

arXiv2024

Imaging the Northern Los Angeles Basins with Autocorrelations

We show reflectivity cross-sections for the San Gabriel, Chino, and San Bernardino basins north of Los Angeles, California determined from autocorrelations of ambient noise and teleseismic earthquake waves. These basins are thought to channel the seismic energy from earthquakes on the San Andreas Fault to Los Angeles and a more accurate model of their depth is important for hazard mitigation. We use the causal side of the autocorrelation function to determine the zero-offset reflection response. To minimize the smoothing effect of the source time function, we remove the common mode from the autocorrelation in order to reveal the zero-offset reflection response. We apply this to 10 temporary nodal lines consisting of a total of 758 geophones with an intraline spacing of 250-300 m. We also show that the autocorrelation function from teleseismic events can provide illumination of subsurface that is consistent with ambient noise. Both autocorrelation results compare favorably to receiver functions.

physics.geo-ph↗

arXiv2023

Deep Neural Helmholtz Operators for 3D Elastic Wave Propagation and Inversion

Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is particularly problematic for full waveform inversion, which typically involves numerous runs of the forward process. In machine learning there has been considerable recent work in the area of operator learning, with a new class of models called neural operators allowing for data-driven solutions to partial differential equations. Recent works in seismology have shown that when neural operators are adequately trained, they can significantly shorten the compute time for wave propagation. However, the memory required for the 3D time domain equations may be prohibitive. In this study, we show that these limitations can be overcome by solving the wave equations in the frequency domain, also known as the Helmholtz equations, since the solutions for a set of frequencies can be determined in parallel. The 3D Helmholtz neural operator is 40 times more memory-efficient than an equivalent time-domain version. We employ a U-shaped neural operator for 2D and 3D elastic wave modeling, achieving two orders of magnitude acceleration compared to a baseline spectral element method. The neural operator accurately generalizes to variable velocity structures and can be evaluated on denser input meshes than used in the training simulations. We also show that when solving for wavefields strictly on the surface, the accuracy can be significantly improved via a graph neural operator layer. In leveraging automatic differentiation, the proposed method can serve as an alternative to the adjoint-state approach for 3D full-waveform inversion, reducing the computation time by a factor of 350.

physics.geo-ph↗