Authors: Ruelmann, Hannes
Geveler, Markus
Turek, Stefan
Title: On the Prospects of Using Machine Learning for the Numerical Simulation of PDEs: Training Neural Networks to Assemble Approximate Inverses
Language (ISO): en
Abstract: In an unconventional approach to combining the very successful Finite Element Methods (FEM) for PDE-based simulation with techniques evolved from the domain of Machine Learning (ML) we employ approximate inverses of the system matrices generated by neural networks in the linear solver. We demonstrate the success of this solver technique on the basis of the Poisson equation which can be seen as a fundamental PDE for many practically relevant simulations [Turek 1999]. We use a basic Richardson iteration applying the approximate inverses generated by fully connected feedforward multilayer perceptrons as preconditioners.
Subject Headings: machine learning
Subject Headings (RSWK): Finite-Elemente-Methode
Maschinelles Lernen
Schwach besetzte Matrix
Issue Date: 2018-02
Appears in Collections:Ergebnisberichte des Instituts für Angewandte Mathematik

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