Deep learning models for global coordinate transformations that linearise PDEs

DOI10.1017/S0956792520000327zbMath1479.35021arXiv1911.02710OpenAlexW3088290697WikidataQ114116642 ScholiaQ114116642MaRDI QIDQ5014841

Steven L. Brunton, Bethany Lusch, Craig Gin, J. Nathan Kutz

Publication date: 8 December 2021

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.02710

zbMATH Keywords

Cole-Hopf transformdeep neural networksKoopman theoryresidual networksautoencoder architecturelinearising transforms

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Theoretical approximation in context of PDEs (35A35)

Related Items

Modern Koopman Theory for Dynamical Systems ⋮ Parsimony as the ultimate regularizer for physics-informed machine learning ⋮ Semi-supervised invertible neural operators for Bayesian inverse problems ⋮ Connections between deep learning and partial differential equations ⋮ Bridging the gap: machine learning to resolve improperly modeled dynamics

Uses Software

• VAMPnets
• PRMLT

Cites Work

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