Hyper-parameter tuning of physics-informed neural networks: Application to Helmholtz problems

We consider physics-informed neural networks (PINNs) (Raissiet al., 2019) for forward physical problems. In order to find optimal PINNs configuration, we introduce a hyper-parameter optimization (HPO) procedure via Gaussian processes-based Bayesian optimization. We apply the HPO to Helmholtz equation for bounded domains and conduct a thorough study, focusing on: (i) performance, (ii) the collocation points density r and (iii) the frequency κ, confirming the applicability and necessity of the method. Numerical experiments are performed in two and three dimensions, including comparison to finite element methods.