A Short Note on Solving Partial Differential Equations Using Convolutional Neural Networks
摘要
Solving partial differential equations (PDEs) is a common task in numerical mathematics and scientific computing. Typical discretization schemes, for example, finite element (FE), finite volume (FV), or finite difference (FD) methods, have the disadvantage that the computations have to be repeated once the boundary conditions (BCs) or the geometry change slightly; typical examples requiring the solution of many similar problems are time-dependent and inverse problems or uncertainty quantification.