Can Physics-Informed Neural Networks beat the Finite Element Method?

• Published in: arXiv.org
• Main Authors: Grossmann, Tamara G, Komorowska, Urszula Julia, Latz, Jonas, Schönlieb, Carola-Bibiane
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 08.02.2023
• Subjects: Accuracy; Approximation; Artificial neural networks; Computing costs; Finite element analysis; Finite element method; Neural networks; Nonlinear differential equations; Numerical methods; Partial differential equations; Physics

Partial differential equations play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences. To simulate such processes and systems, the solutions of PDEs often need to be approximated numerically. The finite element method, for insta...