Towards Generalizable PDE Dynamics Forecasting via Physics-Guided Invariant Learning

Researchers propose iMOOE, a physics-guided invariant learning method for forecasting partial differential equations (PDEs) dynamics with improved zero-shot generalization. The method addresses limitations in existing deep learning approaches that require test-time adaptation by incorporating fundamental physical invariance principles.

• →Current deep learning methods for PDE forecasting struggle with zero-shot out-of-distribution generalization despite using limited training data.
• →The research defines a two-fold PDE invariance principle where ingredient operators and their composition relationships remain consistent across different domains.
• →iMOOE features an Invariance-aligned Mixture Of Operator Expert architecture with frequency-enriched invariant learning objectives.
• →Extensive experiments validate superior in-distribution performance and zero-shot generalization capabilities across diverse forecasting scenarios.
• →The approach eliminates the need for test-time domain-specific adaptation samples required by existing methods.