Out-of-Distribution Generalization for Neural Physics Solvers
This addresses the limitation of neural physics solvers for scientific discovery by enabling reliable extrapolation to novel scenarios, though it appears incremental as it builds on existing methods for generalization.
The paper tackled the problem of poor generalization in neural physics solvers beyond their training data, and introduced NOVA, which achieved 1-2 orders of magnitude lower out-of-distribution errors compared to baselines across complex problems like heat transfer and fluid flow.
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