  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.
