A Local Deep Learning Method for Solving High Order Partial Differential Equations

At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs). But computation high order derivatives neural networks is costly, and lack robustness for training purposes. We propose a novel approach solving PDEs with by simultaneously approximating function value derivatives. introduce intermediate variables rewrite into system low as what done in local discontinuous Galerkin method. The solutions approximated multi-output network. By taking residual loss function, we can optimize network parameters approximate solution. whole process relies on Numerous numerical examples carried out demonstrate that our efficient, robust, flexible, particularly well-suited