Space-time error estimates for deep neural network approximations for differential equations

• Published in: Advances in computational mathematics Vol. 49; no. 1
• Main Authors: Grohs, Philipp, Hornung, Fabian, Jentzen, Arnulf, Zimmermann, Philipp
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2023; Springer Nature B.V
• Subjects: Approximation; Artificial neural networks; Computational mathematics; Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Computer vision; Deep learning; Errors; Estimates; Image classification; Machine learning; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Natural language processing; Neural networks; Object recognition; Partial differential equations; Spacetime; Speech recognition; Visualization; ANNs; Space-time error; PDEs

Over the last few years deep artificial neural networks (ANNs) have very successfully been used in numerical simulations for a wide variety of computational problems including computer vision, image classification, speech recognition, natural language processing, as well as computational advertiseme...