  Solving parametric Partial Differential Equations (PDEs) for a broad range of
parameters is a critical challenge in scientific computing. To this end, neural
operators, which \textcolor{black}{predicts the PDE solution with variable PDE
parameter inputs}, have been successfully used. However, the training of neural
operators typically demands large training datasets, the acquisition of which
can be prohibitively expensive. To address this challenge, physics-informed
training can offer a cost-effective strategy. However, current physics-informed
neural operators face limitations, either in handling irregular domain shapes
or in in generalizing to various discrete representations of PDE parameters. In
this research, we introduce a novel physics-informed model architecture which
can generalize to various discrete representations of PDE parameters and
irregular domain shapes. Particularly, inspired by deep operator neural
networks, our model involves a discretization-independent learning of parameter
embedding repeatedly, and this parameter embedding is integrated with the
response embeddings through multiple compositional layers, for more
expressivity. Numerical results demonstrate the accuracy and efficiency of the
proposed method.
