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The paper presents a method that combines flow‑matching models with energy‑based modeling to explicitly construct scalar energy functions for physical fields. These energies are derived from a matching regression objective on a linear Gaussian interpolation, avoiding variational approximations or extra MCMC steps, and can be used for energy‑corrected data generation, out‑of‑distribution detection, and posterior sampling in inverse problems. The approach enables general MCMC samplers that reduce PDE residuals and spectral distance, and it demonstrates that combining data‑driven and physics‑based energies improves OOD detection accuracy.
arXiv:2609.36527v1 Announce Type: new Abstract: Recovering complete physical fields from sparse observations is challenging because the measurements may not uniquely determine the underlying state. D...
TRACE is a retrospective streaming generative reconstruction framework designed to recover continuous physical fields from sparse, structured sensing streams. It performs approximate Bayesian inference in a continuous-coordinate latent space, fuses sparse off‑grid measurements with a state‑space temporal prior via Kalman‑style filtering, and refines past frames through retrospective smoothing. Experiments on active matter, ocean sound‑speed fields, and supernova simulations demonstrate that TRACE matches or surpasses existing frame‑wise generative reconstructors, offline spatiotemporal methods, and streaming data‑assimilation baselines in reconstruction quality under temporally sparse and spatially localized sensing protocols.
arXiv:2606. 00988v1 Announce Type: new Abstract: Symbolic regression (SR) offers a route to scientific discovery by converting observations into interpretable governing equations.
arXiv:2601. 21284v2 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in engineering and scientific problems where physical laws must be respected.
arXiv:2608.24049v1 Announce Type: new Abstract: Neural operators provide efficient surrogates for spatiotemporal PDE systems, but purely data-driven formulations often accumulate substantial errors d...