  Physics-informed neural network (PINN) has been a prevalent framework for
solving PDEs since proposed. By incorporating the physical information into the
neural network through loss functions, it can predict solutions to PDEs in an
unsupervised manner. However, the design of the neural network structure
basically relies on prior knowledge and experience, which has caused great
trouble and high computational overhead. Therefore, we propose a neural
architecture search-guided method, namely NAS-PINN, to automatically search the
optimum neural architecture for solving certain PDEs. By relaxing the search
space into a continuous one and utilizing masks to realize the addition of
tensors in different shapes, NAS-PINN can be trained through a bi-level
optimization, where the inner loop optimizes the weights and bias of neural
networks and the outer loop the architecture parameters. We verify the ability
of NAS-PINN by several numerical experiments including Poisson, Burgers, and
Advection equations. The characteristics of effective neural architectures for
solving different PDEs are summarized, which can be used to guide the design of
neural networks in PINN. It is found that more hidden layers do not necessarily
mean better performance and sometimes can be harmful. Especially for Poisson
and Advection, a shallow neural network with more neurons is more appropriate
in PINNs. It is also indicated that for complex problems, neural networks with
residual connection can improve the performance of PINNs.
