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

TL;DR

This paper introduces Pseudo Physics-Informed Neural Operators (PPI-NO), a framework that leverages simple, rudimentary physics principles to improve operator learning in data-scarce scenarios, demonstrating significant accuracy gains across benchmarks.

Contribution

The paper presents a novel PPI-NO framework that constructs surrogate physics systems from basic PDEs to enhance neural operator training with limited data.

Findings

Significant accuracy improvements in five benchmark tasks.

Effective in data-scarce scenarios with pseudo-physics guidance.

Demonstrated applicability in fatigue modeling.

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.