Pseudo-Physics-Informed Neural Operators: Enhancing Operator Learning from Limited Data
This addresses a major challenge in surrogate modeling for complex applications where collecting extensive data is expensive, though it is incremental as it builds on existing neural operator methods.
The paper tackles the problem of training neural operators with limited data by proposing the Pseudo Physics-Informed Neural Operator (PPI-NO) framework, which uses surrogate physics from simple PDEs to enhance accuracy, achieving significant improvements in data-scarce scenarios across five benchmark tasks and a fatigue modeling application.
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.