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

Generative models have emerged as a powerful paradigm for solving physics systems and modeling complex spatiotemporal dynamics. However, achieving high physical accuracy without incurring high computational cost remains a fundamental challenge, as existing approaches face a critical speed-fidelity trade-off. In this work, we introduce Recursive Flow Matching (RecFM), a generative framework for forecasting complex spatiotemporal dynamics. RecFM enforces self-consistency to align trajectories across discretization scales, reducing discretization errors and improving performance across metrics for physics-based tasks. To our knowledge, this is the first method to achieve high-fidelity one- and few-step (2-4 step) dynamic generation for scientific systems with performance comparable to state-of-the-art multi-step solvers. Across challenging scientific benchmarks, RecFM achieves up to a 20$\times$ speedup over leading diffusion-based emulators while improving predictive accuracy. Furthermore, RecFM reduces mean squared error by over 15% compared to vanilla flow matching, offering a scalable and efficient solution for real-time scientific emulation.

Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions, while generative approaches better capture details but are costly. Latent-space generative models have emerged as a compromise but with the additional cost of separately pre-trained autoencoders. We propose Wavelet Flow Matching (WFM), a novel generative emulator that overcomes current trade-offs between cost and skill by performing optimal-transport directly in the multi-scale wavelet space. Rather than learning a latent compression, WFM leverages the hierarchical structure of a U-Net to jointly predict transport velocities of a prescribed wavelet representation. On three challenging systems of chaotic fluid dynamics, WFM achieves superior long-horizon stability, accuracy and spectral coherence compared to state-of-the-art models. Our results clearly position the wavelet space as an effective training-free representation for generative emulation of complex physical dynamics.

Physical simulations for intricate geometries with path-dependent constitutive models face difficulties due to the enormous computational cost they require. Recently, the emergence of generative AI models, which succeed in image and video synthesis tasks, has provided a promise to further improve simulations. Although U-Net-based denoising diffusion probabilistic models (DDPMs) have been adopted for elastic stress field generation, they typically require hundreds of sampling steps, and applications of generative models to path-dependent, e.g. plastic, stress fields remain very limited. In this work, we propose a novel flow matching (FM) model based on a transformer backbone for high-resolution path-dependent stress field generation with stochastic loading-unloading paths and geometry. The proposed model operates within the latent space of a variational autoencoder (VAE) and formulates the simulation of plastic fields as a video synthesis task, directly generating the stress fields across all time steps. Meanwhile, we design a non-Gaussian source distribution for flow matching, such that crossings among conditional transport paths are reduced during training. This enables our model to generate satisfactory samples in one step without relying on distillation. In addition, we introduce token-level loading embeddings and two auxiliary networks to further enhance the model performance in path-dependent simulation. The results demonstrate that, even with a limited training dataset, our model can accurately generate high-resolution path-dependent fields. It is much more computationally efficient than finite element analysis, providing a speedup of 6 to 7 times over FEM on CPUs and approximately two orders of magnitude speedup on consumer-grade GPUs.