CW-EDMD improves prediction accuracy by learning local Koopman models for different state-space regions.
problem Inefficient global Koopman operator approximation for distinct local dynamics.
method Cluster-Weighted EDMD (CW-EDMD) learns a soft phase-space partition and per-cluster EDMD operators using EM objective.
result CW-EDMD significantly reduces prediction errors across various systems and configurations.
New theory shows EDMD works well in chaotic systems.
problem Uncertainty in EDMD's properties in chaos.
method Developed rigorous theory of EDMD on chaotic maps using OPUC and transfer operator methods.
result EDMD converges to correct limits in chaotic systems with small polynomial dictionaries.
The paper finds Koopman invariant subspaces using personalized PageRank.
problem Selecting a finite dictionary of observables for Koopman-invariant span.
method Exploiting zero-block structure in EDMD matrices and applying PageRank.
result Personalized PageRank can detect Koopman invariant subspaces.
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a useful data-driven approximation of the Koopman operator for analyzing dynamical syst…
Koopman decomposition is a non-linear generalization of eigen-decomposition, and is being increasingly utilized in the analysis of spatio-temporal dynamics. Well-known techniques such as the dynamic mode decomposition (DMD) and its linear variants provide approximations to the Koopman operator, and have been applied ex…
We present a novel machine learning approach to understanding conformation dynamics of biomolecules. The approach combines kernel-based techniques that are popular in the machine learning community with transfer operator theory for analyzing dynamical systems in order to identify conformation dynamics based on molecula…
We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and stochastic dynamical systems. It can be used for computing eigenvalues, eigenfu…
Optimizes basis functions for learning dynamical systems from data.
problem Learning suitable basis functions for dynamical systems from data.
method Gradient-based optimization framework for learning basis functions.
result Efficacy demonstrated on various benchmark problems.
Koopman-PINN framework improves epidemic model parameter inference and forecasting
problem Epidemic model parameter inference and forecasting
method Combining Koopman operator theory and physics-informed learning
result More accurate parameter estimation, trajectory reconstruction, and long-term forecasting
Noise-robust Koopman operator framework for control with improved stability and performance.
problem Developing a stable and noise-robust Koopman operator for control tasks.
method Proposes a learning framework using Hankel matrix and neural network approximations for system dynamics, ensuring long-term stability and noise robustness.
result Demonstrates improved model performance and noise robustness in control tasks compared to existing methods.
KOMET identifies Koopman operators from model parameter trajectories to adapt to evolving data distributions.
problem Adaptation of parametric models to non-stationary environments.
method Data-driven framework using Koopman operator identification and Extended Dynamic Mode Decomposition (EDMD).
result KOMET achieves high autonomous-rollout accuracies of 0.981 to 1.000 over 100 time steps on various drifting datasets.
Unified kernel framework extends to stochastic systems, improving numerical stability.
problem Extending kernel methods to stochastic dynamical systems with diffusion.
method Unified kernel framework, Feynman-Kac path-integral representations, collocation-based computational framework.
result Kernel equivalence under uniform ellipticity assumptions and improved numerical stability with moderate diffusion.
Paper introduces method to estimate animal motion on unknown submanifolds using Koopman operator.
problem Estimating animal motion on unknown submanifolds in high-dimensional space.
method Data-dependent approximation of Koopman operator in RKHS over ambient space.
result Strong rates of convergence derived for estimates in terms of fill distance.
Enhances Koopman operator estimation with intrinsic observables in RKHS.
problem Accurate estimation of Koopman operator and its spectrum.
method Jet Extended Dynamic Mode Decomposition (JetEDMD) leveraging RKHS jets.
result Proves JetEDMD's superiority with error bounds and convergence rate.