Out-of-Distribution Generalization for Neural Physics Solvers

TL;DR

NOVA is a novel neural physics solver that significantly improves out-of-distribution generalization, enabling accurate long-term predictions and design exploration in complex physical systems.

Contribution

We introduce NOVA, a physics-aligned neural network framework that enhances out-of-distribution generalization for solving PDEs in scientific discovery.

Findings

Achieves 1-2 orders of magnitude lower out-of-distribution errors than baselines.

Stabilizes long-time dynamical simulations.

Improves generative design in nonlinear systems.

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