A Koopman-Takens theorem: linear least squares prediction of nonlinear time series

Dynamical aspects of measure-preserving transformations (37A05) Ergodic theory of linear operators (47A35) Time series analysis of dynamical systems (37M10) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30) Nonlinear ergodic theorems (47H25)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
On the computation of attractors for delay differential equations
Dynamical systems of continuous spectra
Hamiltonian systems and transformations in Hilbert space.
Bessel orbits of normal operators
Lyapunov exponents of two stochastic Lorenz 63 systems
The Lorenz attractor is mixing
A data-driven approximation of the koopman operator: extending dynamic mode decomposition
Noise reduction: Finding the simplest dynamical system consistent with the data
Extracting qualitative dynamics from experimental data
Embedology
Zur Operatorenmethode in der klassischen Mechanik
The reconstruction theorem for endomorphisms
On convergence of extended dynamic mode decomposition to the Koopman operator
Supervised learning from noisy observations: combining machine-learning techniques with data assimilation
Kernel-based prediction of non-Markovian time series
On the Shroer-Sauer-Ott-Yorke predictability conjecture for time-delay embeddings
Data-driven model reduction, Wiener projections, and the Koopman-Mori-Zwanzig formalism
Delay-coordinate maps, coherence, and approximate spectra of evolution operators
Data-driven spectral analysis of the Koopman operator
Delay-coordinate maps and the spectra of Koopman operators
A mathematical framework for quantifying predictability through relative entropy
Typical dynamics of volume preserving homeomorphisms
Takens' embedding theorem with a continuous observable
Dynamic mode decomposition of numerical and experimental data
Spectral Analysis for Physical Applications
Spectral analysis of nonlinear flows
Transformations With Discrete Spectrum are Stacking Transformations
Some Pointwise Convergence Results in L^p(μ), 1 < p < ∞
One-Parameter Semigroups for Linear Evolution Equations
Systems of finite rank
A priori estimation of memory effects in reduced-order models of nonlinear systems using the Mori–Zwanzig formalism
Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator
Time-Delay Observables for Koopman: Theory and Applications
A probabilistic Takens theorem
Subsequence bounded rational ergodicity of rank-one transformations
Operator Theoretic Aspects of Ergodic Theory
Strictly Proper Scoring Rules, Prediction, and Estimation
Transport, Collective Motion, and Brownian Motion
Power spectra for deterministic chaotic dynamical systems
APPROXIMATIONS IN ERGODIC THEORY
A topological delay embedding theorem for infinite-dimensional dynamical systems
Synchronization of reconstructed dynamical systems
Residual dynamic mode decomposition: robust and verified Koopmanism
Spectral theory of dynamical systems
Regression-Based Projection for Learning Mori–Zwanzig Operators
The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems
Rigorous data‐driven computation of spectral properties of Koopman operators for dynamical systems
Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations

This page was built for publication: A Koopman-Takens theorem: linear least squares prediction of nonlinear time series