  Recent advances in deep learning for solving partial differential equations
(PDEs) have introduced physics-informed neural networks (PINNs), which
integrate machine learning with physical laws. Physics-informed convolutional
neural networks (PICNNs) extend PINNs by leveraging CNNs for enhanced
generalization and efficiency. However, current PICNNs depend on manual design,
and inappropriate designs may not effectively solve PDEs. Furthermore, due to
the diversity of physical problems, the ideal network architectures and loss
functions vary across different PDEs. It is impractical to find the optimal
PICNN architecture and loss function for each specific physical problem through
extensive manual experimentation. To surmount these challenges, this paper uses
automated machine learning (AutoML) to automatically and efficiently search for
the loss functions and network architectures of PICNNs. We introduce novel
search spaces for loss functions and network architectures and propose a
two-stage search strategy. The first stage focuses on searching for factors and
residual adjustment operations that influence the loss function, while the
second stage aims to find the best CNN architecture. Experimental results show
that our automatic searching method significantly outperforms the
manually-designed model on multiple datasets.
