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.

Thermal-fluid field distributions underpin the analysis and operation of energy infrastructure, from nuclear-reactor cooling channels to industrial heat exchangers, but resolving these distributions through computational fluid dynamics requires prohibitively large simulation ensembles. Their complex geometries also demand unstructured meshes that are poorly accommodated by generative models developed for regular grids. Here we introduce FlowMesh, a generative framework that combines permutation-invariant mesh encoding with deterministic latent flow matching and an l1 penalty on the learned transport velocity. FlowMesh generates full-field realizations directly on fixed unstructured meshes without auxiliary grid interpolation or a stochastic denoising chain. Across lid-driven-cavity, pressurized-water-reactor subchannel and heat-exchanger datasets, evaluated over six matched training seeds, FlowMesh achieves macro-averaged probability-density-function coverage of 91.7%-97.0%, exceeding an architecture-controlled latent diffusion model by $11.6$--$45.4$ percentage points. Latent-velocity regularization increases coverage by $3.8$ percentage points for reactor flows and 1.1 points for heat-exchanger flows, while reducing temperature-field Kullback--Leibler divergence by 1.7-2.4-fold. Each full-field realization requires 1.23 \pm 0.15 s, providing a 585--1902-fold wall-clock acceleration over computational fluid dynamics. FlowMesh therefore makes large-scale generative characterization of thermal-fluid states computationally feasible, providing a foundation for data-driven analysis and digital-twin development in fixed-geometry energy systems.

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.