Pseudo Physics-Informed Neural Operators
Keywords: Pseudo Physics, Data-Driven Physics Discovery, PDEs, Neural Operator, AI for science, Scientific Machine Learning
Abstract: Recent advancements in operator learning are transforming the landscape of computational physics and engineering, especially alongside the rapidly evolving field of physics-informed machine learning. The convergence of these areas offers
exciting opportunities for innovative research and applications. However, merging
these two realms often demands deep expertise and explicit knowledge of physical systems, which may be challenging or even impractical in relatively complex applications. To address this limitation, we propose a novel framework: Pseudo
Physics-Informed Neural Operator (PPI-NO). In this framework, we construct a
surrogate physics system for the target system using partial differential equations
(PDEs) derived from simple, rudimentary physics knowledge, such as basic differential operators. We then couple the surrogate system with the neural operator model, utilizing an alternating update and learning process to iteratively enhance
the model’s predictive power. While the physics derived via PPI-NO may not mirror the ground-truth underlying physical laws — hence the term “pseudo physics” — this approach significantly enhances the accuracy of current operator learning
models, particularly in data scarce scenarios. Through extensive evaluations across
five benchmark operator learning tasks and an application in fatigue modeling,
PPI-NO consistently outperforms competing methods by a significant margin. The
success of PPI-NO may introduce a new paradigm in physics-informed machine
learning, one that requires minimal physics knowledge and opens the door to
broader applications in data-driven physics learning and simulations.
Primary Area: other topics in machine learning (i.e., none of the above)
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Submission Number: 4999
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