On the latent dimension of deep autoencoders for reduced order modeling of PDEs parametrized by random fields

• Published in: Advances in computational mathematics Vol. 50; no. 5
• Main Authors: Franco, Nicola Rares, Fraulin, Daniel, Manzoni, Andrea, Zunino, Paolo
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2024; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Deep learning; Error analysis; Fields (mathematics); Impact analysis; Machine learning; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Neural networks; Parameterization; Partial differential equations; Reduced order models; Stochastic processes; Visualization; Deep learning; Random fields; Autoencoders; Reduced order modeling; 35A35; 35B30; 68T07; Parametrized PDEs; 65N30
• ISSN: 1019-7168; 1572-9044
• DOI: 10.1007/s10444-024-10189-6

Deep Learning is having a remarkable impact on the design of Reduced Order Models (ROMs) for Partial Differential Equations (PDEs), where it is exploited as a powerful tool for tackling complex problems for which classical methods might fail. In this respect, deep autoencoders play a fundamental rol...