Solving Parametric PDEs with Radial Basis Functions and Deep Neural Networks

arXiv:2404.06834v1 Announce Type: cross
Abstract: We propose the POD-DNN, a novel algorithm leveraging deep neural networks (DNNs) along with radial basis functions (RBFs) in the context of the proper orthogonal decomposition (POD) reduced basis method (RBM), aimed at approximating the parametric mapping of parametric partial differential equations on irregular domains. The POD-DNN algorithm capitalizes on the low-dimensional characteristics of the solution manifold for parametric equations, alongside the inherent offline-online computational strategy of RBM and DNNs. In numerical experiments, POD-DNN demonstrates …

abstract algorithm arxiv context cs.lg cs.na differential dnn functions mapping math.na networks neural networks novel parametric pod type