arXiv:2509.26282 · v2

Benchmarking Stochastic Interpolants for Modeling Physical Systems

首次提交 2025-09-30 22:02

版本更新 2026-11-10 06:06

雷达观测 2026-11-11 11:04

摘要

Generative models have recently emerged as powerful surrogates for physical systems, demonstrating increased accuracy, stability, and/or statistical fidelity. However, most approaches rely on iteratively denoising a Gaussian, a choice that may not be the most effective for autoregressive prediction tasks, where the current and future states are often closely related. We therefore benchmark generative models based on stochastic interpolants, which can learn maps between arbitrary densities, against standard Gaussian-denoising frameworks across a range of fluid and climate systems. Following prior work, we consider a transport map for dynamical systems that learns an interpolant between a point mass at the current state and a conditional distribution of future states. We find that stochastic interpolants can match or outperform Gaussian-denoising baselines in pointwise accuracy, spectral fidelity, and probabilistic skill. Furthermore, we identify a tradeoff where deterministic sampling can improve pointwise accuracy but smooth predictions, whereas stochastic sampling recovers spectral content and calibration but requires more function evaluations, as well as ensemble averaging to recover pointwise accuracy. As a whole, these results establish stochastic interpolants as a competitive baseline for generative physical emulation, and also indicate that the training loss, sampler, and transport map should be chosen with the physical system and target metric in mind.

作者备注：Code and data is available at http://github.com/anthonyzhou-1/interpolant_pdes