Physics-Informed Geometry-Aware Neural Operator
This addresses a bottleneck in engineering design by enabling more flexible and cost-effective PDE solution predictions, though it appears incremental as it builds on existing neural operator frameworks.
The paper tackles the challenge of training neural operators for parametric PDEs under variable parameters and domain geometries without requiring large datasets, by introducing PI-GANO, which achieves accurate and efficient generalization across both aspects.
Engineering design problems often involve solving parametric Partial Differential Equations (PDEs) under variable PDE parameters and domain geometry. Recently, neural operators have shown promise in learning PDE operators and quickly predicting the PDE solutions. However, training these neural operators typically requires large datasets, the acquisition of which can be prohibitively expensive. To overcome this, physics-informed training offers an alternative way of building neural operators, eliminating the high computational costs associated with Finite Element generation of training data. Nevertheless, current physics-informed neural operators struggle with limitations, either in handling varying domain geometries or varying PDE parameters. In this research, we introduce a novel method, the Physics-Informed Geometry-Aware Neural Operator (PI-GANO), designed to simultaneously generalize across both PDE parameters and domain geometries. We adopt a geometry encoder to capture the domain geometry features, and design a novel pipeline to integrate this component within the existing DCON architecture. Numerical results demonstrate the accuracy and efficiency of the proposed method. All the codes and data related to this work are available on GitHub: https://github.com/WeihengZ/Physics-informed-Neural-Foundation-Operator.