论文标题
物理知识神经网络的超参数调整：应用于Helmholtz问题
Hyper-parameter tuning of physics-informed neural networks: Application to Helmholtz problems
论文作者
论文摘要
我们考虑物理信息的神经网络（PINN）[Raissi等，J。〜Comput。物理。 278（2019）686-707]用于前进的身体问题。为了找到最佳的PINNS配置，我们通过基于高斯流程的贝叶斯优化引入了超参数优化（HPO）程序。我们将HPO应用于Helmholtz方程进行有限域，并进行详尽的研究，重点是：（i）绩效，（ii）搭配点密度$ r $和（iii）频率$κ$，确认该方法的适用性和必要性。数值实验在两个和三个维度上进行，包括与有限元方法的比较。
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 $κ$, confirming the applicability and necessity of the method. Numerical experiments are performed in two and three dimensions, including comparison to finite element methods.
