A Short Note on Solving Partial Differential Equations Using Convolutional Neural Networks

Conference paper (2024)

Authors

Viktor Grimm University of Cologne
A. Heinlein Numerical Analysis - EEMCS
Axel Klawonn University of Cologne
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2024 Viktor Grimm, A. Heinlein, Axel Klawonn
DOI: https://doi.org/10.1007/978-3-031-50769-4_1
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Published Date

2024

Language

English

Reuse Rights

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

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.