Neural operator improves physics informed neural network accuracy outside training range
Learning Physics from an Imperfect Ancestor
Machine Learning
Summary
When computers try to solve complicated physics problems, they can get stuck on wrong answers even if their calculations look good. The authors found a way to fix this by using a rough guide from one type of computer model to help another model start closer to the right answer. Then, the second model double-checks and improves the solution so it becomes accurate. This method works well on several physics problems where traditional methods either fail or take a long time to get right.
What this means in practice
- •For computational fluid dynamics engineers: Speed up and improve accuracy of fluid flow simulations at physical conditions outside prior data ranges.
- •For engineering simulation developers: Implement a hybrid modeling approach combining rough neural operators with physics-informed networks to handle nonlinear PDEs effectively.
Authors
S. Mohammad Mousavi, Teeratorn Kadeethum, Nikolaos Bouklas, Somdatta Goswami
Abstract
Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed neural networks avoid dependence on labeled data, yet their optimization can be basin-fragile: when the governing residual admits multiple solutions, a PINN trained from scratch may converge to a physically incorrect state despite achieving a small residual. We show that these failure modes can be addressed jointly: an imperfect NO provides the structural prior needed to place a PINN in the correct solution basin, while the PDE residual refines the solution beyond the operator's accuracy. We introduce a three-stage framework that freezes the spatial basis of a physics-informed NO, extrapolates its solution branch to an out-of-distribution parameter using a polynomial continuation prior, and distills the resulting field into a fresh PINN. The NO need not be accurate at the target; it transfers solution-branch information, while PDE residual minimization in the PINN governs convergence. We evaluate the framework on three nonlinear PDEs: 1D viscous Burgers, 2D steady Allen-Cahn near a pitchfork bifurcation, and 2D steady lid-driven cavity flow. For Allen-Cahn, where the trivial solution satisfies the PDE residual exactly, a standard PINN collapses to the trivial zero branch, whereas distillation from the crude extrapolated operator recovers the non-trivial branch that matches the finite-difference reference. For the lid-driven cavity, extrapolating to a Reynolds number of Re = 3200 accelerates convergence to the correct physical state, achieving competitive accuracy using fewer parameters and optimization steps than recent literature baselines. These results establish a simple principle: an NO need not accurately predict the solution to be useful; it only needs to identify the correct basin from which PINN optimization can recover it.