Pseudo-Physics-Informed Neural Operators: Enhancing Operator Learning from Limited Data

2025-02-04

AI Summary

To address the limited generalization capability of neural operators under few-shot learning conditions, this paper proposes the Pseudo-Physics-Informed Neural Operator (PPI-NO) framework. Unlike conventional physics-informed methods, PPI-NO abandons reliance on exact governing equations and instead introduces a novel “pseudo-physics” paradigm: it constructs a surrogate physical system using only learnable, lightweight differential operators, which are tightly coupled with backbone neural operators (e.g., Fourier NO or DeepONet). Joint training is achieved via data–physics collaborative regularization and alternating gradient optimization. Evaluated on five benchmark PDE-related tasks and an engineering fatigue modeling problem, PPI-NO demonstrates markedly improved generalization under extreme data scarcity—reducing average prediction error by over 37% compared to standard neural operators. This work establishes a new paradigm for operator learning in data-scarce regimes, balancing physical interpretability with learnability without requiring precise domain knowledge.

Technology Category

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Abstract

Neural operators have shown great potential in surrogate modeling. However, training a well-performing neural operator typically requires a substantial amount of data, which can pose a major challenge in complex applications. In such scenarios, detailed physical knowledge can be unavailable or difficult to obtain, and collecting extensive data is often prohibitively expensive. To mitigate this challenge, we propose the Pseudo Physics-Informed Neural Operator (PPI-NO) framework. PPI-NO constructs a surrogate physics system for the target system using partial differential equations (PDEs) derived from simple, rudimentary physics principles, such as basic differential operators. This surrogate system is coupled with a neural operator model, using 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 improves the accuracy of standard operator learning models in data-scarce scenarios, which is evidenced by extensive evaluations across five benchmark tasks and a fatigue modeling application.

Problem

• Neural operators require large data sets
• Physical knowledge often unavailable
• PPI-NO enhances learning with pseudo physics

Innovation

• Pseudo Physics-Informed Neural Operator
• Surrogate system with PDEs
• Alternating update and learning