Discovery of Dynamics Using Linear Multistep Methods

DOI10.1137/19M130981XzbMath1466.65050arXiv1912.12728OpenAlexW3129782742MaRDI QIDQ5151929

Qiang Du, Rachael T. Keller

Publication date: 23 February 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.12728

zbMATH Keywords

artificial intelligencelinear multistep methodsstability and convergencelearning dynamicsdata-driven modelingroot conditiondiscovery of dynamics

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Artificial intelligence (68T99) Numerical solution of inverse problems involving ordinary differential equations (65L09)

Related Items

Weak SINDy for partial differential equations ⋮ Discovery of subdiffusion problem with noisy data via deep learning ⋮ VPNets: volume-preserving neural networks for learning source-free dynamics ⋮ The Discovery of Dynamics via Linear Multistep Methods and Deep Learning: Error Estimation ⋮ Data-driven sparse identification of nonlinear dynamical systems using linear multistep methods ⋮ Deep Neural Networks for Solving Large Linear Systems Arising from High-Dimensional Problems ⋮ A framework for machine learning of model error in dynamical systems ⋮ Deep-OSG: deep learning of operators in semigroup ⋮ Weak SINDy: Galerkin-Based Data-Driven Model Selection ⋮ Inferring switched nonlinear dynamical systems ⋮ Kernel-based parameter estimation of dynamical systems with unknown observation functions

Uses Software

• RODAS
• PMTK
• ImageNet
• torchdiffeq
• PDE-Net
• AlexNet
• PRMLT

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