Can physics-informed neural networks beat the finite element method?

• Published in: IMA journal of applied mathematics Vol. 89; no. 1; pp. 143 - 174
• Main Authors: Grossmann, Tamara G, Komorowska, Urszula Julia, Latz, Jonas, Schönlieb, Carola-Bibiane
• Format: Journal Article
• Language: English
• Published: England Oxford University Press 01.01.2024
• Subjects: Original Papers; deep learning; finite element method; partial differential equations; physics-informed neural networks

Partial differential equations (PDEs) 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, fo...