Modern Koopman theory for dynamical systems
The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …
algorithms emerging from modern computing and data science. First-principles derivations …
The mpEDMD algorithm for data-driven computations of measure-preserving dynamical systems
MJ Colbrook - SIAM Journal on Numerical Analysis, 2023 - SIAM
Koopman operators globally linearize nonlinear dynamical systems and their spectral
information is a powerful tool for the analysis and decomposition of nonlinear dynamical …
information is a powerful tool for the analysis and decomposition of nonlinear dynamical …
Rigorous data‐driven computation of spectral properties of Koopman operators for dynamical systems
Koopman operators are infinite‐dimensional operators that globally linearize nonlinear
dynamical systems, making their spectral information valuable for understanding dynamics …
dynamical systems, making their spectral information valuable for understanding dynamics …
A framework for machine learning of model error in dynamical systems
The development of data-informed predictive models for dynamical systems is of
widespread interest in many disciplines. We present a unifying framework for blending …
widespread interest in many disciplines. We present a unifying framework for blending …
Ensemble Kalman methods: a mean field perspective
This paper provides a unifying mean field based framework for the derivation and analysis of
ensemble Kalman methods. Both state estimation and parameter estimation problems are …
ensemble Kalman methods. Both state estimation and parameter estimation problems are …
Kernel learning for robust dynamic mode decomposition: linear and nonlinear disambiguation optimization
Research in modern data-driven dynamical systems is typically focused on the three key
challenges of high dimensionality, unknown dynamics and nonlinearity. The dynamic mode …
challenges of high dimensionality, unknown dynamics and nonlinearity. The dynamic mode …
Operator inference with roll outs for learning reduced models from scarce and low-quality data
Data-driven modeling has become a key building block in computational science and
engineering. However, data that are available in science and engineering are typically …
engineering. However, data that are available in science and engineering are typically …
The multiverse of dynamic mode decomposition algorithms
MJ Colbrook - arxiv preprint arxiv:2312.00137, 2023 - arxiv.org
Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to
decompose complex, nonlinear systems into a set of modes, revealing underlying patterns …
decompose complex, nonlinear systems into a set of modes, revealing underlying patterns …
Ensemble Kalman inversion for sparse learning of dynamical systems from time-averaged data
Enforcing sparse structure within learning has led to significant advances in the field of data-
driven discovery of dynamical systems. However, such methods require access not only to …
driven discovery of dynamical systems. However, such methods require access not only to …
Data assimilation in operator algebras
We develop an algebraic framework for sequential data assimilation of partially observed
dynamical systems. In this framework, Bayesian data assimilation is embedded in a …
dynamical systems. In this framework, Bayesian data assimilation is embedded in a …