  Physics-informed neural networks (PINNs) are revolutionizing science and
engineering practice by bringing together the power of deep learning to bear on
scientific computation. In forward modeling problems, PINNs are meshless
partial differential equation (PDE) solvers that can handle irregular,
high-dimensional physical domains. Naturally, the neural architecture
hyperparameters have a large impact on the efficiency and accuracy of the PINN
solver. However, this remains an open and challenging problem because of the
large search space and the difficulty of identifying a proper search objective
for PDEs. Here, we propose Auto-PINN, the first systematic, automated
hyperparameter optimization approach for PINNs, which employs Neural
Architecture Search (NAS) techniques to PINN design. Auto-PINN avoids manually
or exhaustively searching the hyperparameter space associated with PINNs. A
comprehensive set of pre-experiments using standard PDE benchmarks allows us to
probe the structure-performance relationship in PINNs. We find that the
different hyperparameters can be decoupled, and that the training loss function
of PINNs is a good search objective. Comparison experiments with baseline
methods demonstrate that Auto-PINN produces neural architectures with superior
stability and accuracy over alternative baselines.
