Reframing Generative Models for Physical Systems using Stochastic Interpolants

Anthony Zhou, Alexander Wikner, Amaury Lancelin, Pedram Hassanzadeh, Amir Barati Farimani

Keywords: Neural PDE Surrogates, Weather Forecasting, Climate, PDEs, Stochastic Interpolants, Generative Models

TL;DR: We benchmark generative models on physical systems and establish stochastic interpolants as a strong baseline.

Abstract: 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 in PDEs and dynamical systems such as climate. Given the proximity of current and future distributions in these tasks, we consider generative models based on stochastic interpolants, which can directly learn maps between arbitrary densities. To evaluate this framework, we benchmark a variety of generative models across fluid and climate systems. Our experiments suggest that stochastic interpolants can use fewer sampling steps and produce more accurate predictions than models relying on transporting Gaussian noise. We also observe broad trends across generative models, such as the ability to exchange deterministic accuracy, spectral consistency, and probabilistic calibration through sampling. Given these results, this study establishes stochastic interpolants as a competitive baseline for physical emulation and gives insight into the abilities of different generative modeling frameworks.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

Submission Number: 19329