We consider physics-informed neural networks (PINNs) [Raissi et al., J.~Comput. Phys. 278 (2019) 686-707] 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 $\kappa$, confirming the applicability and necessity of the method. Numerical experiments are performed in two and three dimensions, including comparison to finite element methods.

翻译：针对正演物理问题，本文考虑物理信息神经网络（PINNs）[Raissi 等，J.~Comput. Phys. 278 (2019) 686-707]。为寻找最优PINNs配置，我们引入基于高斯过程的贝叶斯优化超参数优化（HPO）流程。将该HPO方法应用于有界域亥姆霍兹方程，并开展系统研究，重点关注：(i) 性能表现，(ii) 配置点密度 $r$，(iii) 频率 $\kappa$，验证了该方法的适用性与必要性。数值实验涵盖二维与三维场景，并与有限元方法进行了对比分析。