Out-of-Distribution Generalization for Neural Physics Solvers

2026-01-27

AI Summary

Neural physics solvers often exhibit limited generalization under out-of-distribution (OOD) conditions, hindering their applicability to novel design exploration and long-term prediction. To address this challenge, this work proposes NOVA, a method that learns physics-aligned representations from sparse initial data, enabling efficient generalization across OOD variations in PDE parameters, geometric configurations, and initial conditions. NOVA achieves the first reliable extrapolation of neural solvers to previously unseen physical scenarios, substantially enhancing the stability of long-time dynamical simulations and generative design capabilities. Evaluated on nonlinear systems—including heat conduction, reaction–diffusion, and fluid flow—NOVA reduces OOD errors by one to two orders of magnitude compared to data-driven baselines and demonstrates successful applications in Turing pattern simulation and microfluidic device optimization.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Low Level & Physics-based Vision
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Neural physics solvers are increasingly used in scientific discovery, given their potential for rapid in silico insights into physical, materials, or biological systems and their long-time evolution. However, poor generalization beyond their training support limits exploration of novel designs and long-time horizon predictions. We introduce NOVA, a route to generalizable neural physics solvers that can provide rapid, accurate solutions to scenarios even under distributional shifts in partial differential equation parameters, geometries and initial conditions. By learning physics-aligned representations from an initial sparse set of scenarios, NOVA consistently achieves 1-2 orders of magnitude lower out-of-distribution errors than data-driven baselines across complex, nonlinear problems including heat transfer, diffusion-reaction and fluid flow. We further showcase NOVA's dual impact on stabilizing long-time dynamical rollouts and improving generative design through application to the simulation of nonlinear Turing systems and fluidic chip optimization. Unlike neural physics solvers that are constrained to retrieval and/or emulation within an a priori space, NOVA enables reliable extrapolation beyond known regimes, a key capability given the need for exploration of novel hypothesis spaces in scientific discovery

Problem

• Out-of-Distribution Generalization
• Neural Physics Solvers
• Distributional Shift
• Long-time Prediction
• Scientific Discovery

Innovation

• out-of-distribution generalization
• neural physics solvers
• physics-aligned representations
• distributional shift
• generative design