Towards Generalizable PDE Dynamics Forecasting via Physics-Guided Invariant Learning

• URL: http://arxiv.org/abs/2509.24332v1
• Date: Mon, 29 Sep 2025 06:30:01 GMT
• Title: Towards Generalizable PDE Dynamics Forecasting via Physics-Guided Invariant Learning
• Authors: Siyang Li, Yize Chen, Yan Guo, Ming Huang, Hui Xiong,
• Abstract summary: We propose a physics-guided invariant learning method termed iMOOE.<n>iMOOE features an Invariance-aligned Mixture Of Expert architecture and a frequency-enriched invariant learning objective.<n>Experiments validate iMOOE's superior in-distribution performance and zero-shot generalization capabilities on diverse OOD forecasting scenarios.
• Score: 16.66374733932547
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Advanced deep learning-based approaches have been actively applied to forecast the spatiotemporal physical dynamics governed by partial differential equations (PDEs), which acts as a critical procedure in tackling many science and engineering problems. As real-world physical environments like PDE system parameters are always capricious, how to generalize across unseen out-of-distribution (OOD) forecasting scenarios using limited training data is of great importance. To bridge this barrier, existing methods focus on discovering domain-generalizable representations across various PDE dynamics trajectories. However, their zero-shot OOD generalization capability remains deficient, since extra test-time samples for domain-specific adaptation are still required. This is because the fundamental physical invariance in PDE dynamical systems are yet to be investigated or integrated. To this end, we first explicitly define a two-fold PDE invariance principle, which points out that ingredient operators and their composition relationships remain invariant across different domains and PDE system evolution. Next, to capture this two-fold PDE invariance, we propose a physics-guided invariant learning method termed iMOOE, featuring an Invariance-aligned Mixture Of Operator Expert architecture and a frequency-enriched invariant learning objective. Extensive experiments across simulated benchmarks and real-world applications validate iMOOE's superior in-distribution performance and zero-shot generalization capabilities on diverse OOD forecasting scenarios.

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