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

Understand

At present, deep learning based methods are being employed to resolve the computational challenges of high-dimensional partial differential equations (PDEs).

• But the computation of the high order derivatives of neural networks is costly, and high order derivatives lack robustness for training purposes.
• We propose a novel approach to solving PDEs with high order derivatives by simultaneously approximating the function value and derivatives.
• We introduce intermediate variables to rewrite the PDEs into a system of low order differential equations as what is done in the local discontinuous Galerkin method.