Regression-Based Projection for Learning Mori–Zwanzig Operators

DOI10.1137/22m1506146arXiv2205.05135OpenAlexW4387617664MaRDI QIDQ6084965

Yen Ting Lin, Yifeng Tian, Danny Perez, Daniel Livescu

Publication date: 2 December 2023

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.05135

zbMATH Keywords

neural networksregressionKoopman representationMori-Zwanzig formalismdata-driven learningnonlinear projection operators

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Approximation methods and numerical treatment of dynamical systems (37M99) Applications of functional analysis in statistical physics (46N55)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Discovering governing equations from data by sparse identification of nonlinear dynamical systems
• Applications of the dynamic mode decomposition
• A data-driven approximation of the koopman operator: extending dynamic mode decomposition
• Optimal prediction with memory
• A dynamic subgrid scale model for large eddy simulations based on the Mori-Zwanzig formalism
• Kernel-based prediction of non-Markovian time series
• Lift \& learn: physics-informed machine learning for large-scale nonlinear dynamical systems
• Data-driven model reduction, Wiener projections, and the Koopman-Mori-Zwanzig formalism
• Machine learning for prediction with missing dynamics
• Dynamic mode decomposition of numerical and experimental data
• Spectral analysis of nonlinear flows
• Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
• On Flame Propagation Under Conditions of Stoichiometry
• Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator
• Deterministic Nonperiodic Flow
• Renormalized Reduced Order Models with Memory for Long Time Prediction
• Some Recent Developments in Turbulence Closure Modeling
• Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator
• Dynamical Systems of Continuous Spectra
• Erratum: “On explaining the surprising success of reservoir computing forecaster of chaos? The universal machine learning dynamical system with contrasts to VAR and DMD” [Chaos 31(1), 013108 (2021)]
• Data-Driven Learning for the Mori--Zwanzig Formalism: A Generalization of the Koopman Learning Framework
• SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics
• Model Reduction with Memory and the Machine Learning of Dynamical Systems
• LYAPUNOV EXPONENTS OF THE KURAMOTO–SIVASHINSKY PDE
• Mathematics for Machine Learning
• Fourth-Order Time-Stepping for Stiff PDEs
• Transport, Collective Motion, and Brownian Motion
• Reproducing Kernel Hilbert Spaces for Penalized Regression: A Tutorial