Enhancing predictive capabilities in data-driven dynamical modeling with automatic differentiation: Koopman and neural ODE approaches

DOI10.1063/5.0180415zbMATH Open1546.37136MaRDI QIDQ6554429

Author name not available (Why is that?), C. Ricardo Constante-Amores, Michael D. Graham

Publication date: 12 June 2024

Published in: Chaos (Search for Journal in Brave)

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Learning and adaptive systems in artificial intelligence (68T05) Time series analysis of dynamical systems (37M10)

Cites Work

• Title not available (Why is that?)
• A kernel-based method for data-driven Koopman spectral analysis
• Hamiltonian systems and transformations in Hilbert space.
• On the history of the isomorphism problem of dynamical systems with special regard to von Neumann's contribution
• Exponential time differencing for stiff systems
• A data-driven approximation of the koopman operator: extending dynamic mode decomposition
• Applied Koopman theory for partial differential equations and data-driven modeling of spatio-temporal systems
• Stabilized neural ordinary differential equations for long-time forecasting of dynamical systems
• Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders
• Spectral properties of dynamical systems, model reduction and decompositions
• A generalized solution of the orthogonal Procrustes problem
• Nonlinear dynamics and chaos. With applications to physics, biology, chemistry, and engineering
• Applied Koopmanism
• Dynamic mode decomposition of numerical and experimental data
• Spectral analysis of nonlinear flows
• A hierarchy of low-dimensional models for the transient and post-transient cylinder wake
• Smooth Random Functions, Random ODEs, and Gaussian Processes
• Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator
• On the derivative of the generalized inverse of a matrix
• Introduction to Dynamical Systems
• Analysis of Fluid Flows via Spectral Properties of the Koopman Operator
• Constrained sparse Galerkin regression
• Koopman mode expansions between simple invariant solutions
• Data Assimilation
• Linearly Recurrent Autoencoder Networks for Learning Dynamics
• Koopman-mode decomposition of the cylinder wake
• The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate
• Residual dynamic mode decomposition: robust and verified Koopmanism
• Dynamics of a data-driven low-dimensional model of turbulent minimal Couette flow
• The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems
• Koopman Operator Inspired Nonlinear System Identification
• Deep learning enhanced dynamic mode decomposition
• Data-driven reduced-order modeling of spatiotemporal chaos with neural ordinary differential equations

Related Items (1)

Representing turbulent statistics with partitions of state space. I: Theory and methodology

This page was built for publication: Enhancing predictive capabilities in data-driven dynamical modeling with automatic differentiation: Koopman and neural ODE approaches

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6554429)