109 citations · 848 across the 38 of their papers we have counts for
43 papers
Revealing trends and persistent cycles of non-autonomous systems with operator-theoretic techniques: Applications to past and present climate dynamics
Gary Froyland, Dimitrios Giannakis, Edoardo Luna +1
An important problem in modern applied science is characterizing the behavior of systems with complex internal dynamics subjected to external forcings from their environment. While…
Koopman spectral analysis of skew-product dynamics on Hilbert -modules
Dimitrios Giannakis, Yuka Hashimoto, Masahiro Ikeda +2
We introduce a linear operator on a Hilbert -module for analyzing skew-product dynamical systems. The operator is defined by composition and multiplication. We show that it ad…
Quantum Mechanics for Closure of Dynamical Systems
David Freeman, Dimitrios Giannakis, Joanna Slawinska
We propose a scheme for data-driven parameterization of unresolved dimensions of dynamical systems based on the mathematical framework of quantum mechanics and Koopman operator the…
Data Assimilation in Operator Algebras
David Freeman, Dimitrios Giannakis, Brian Mintz +2
We develop an algebraic framework for sequential data assimilation of partially observed dynamical systems. In this framework, Bayesian data assimilation is embedded in a non-abeli…
Graph-theoretic algorithms for Kolmogorov operators: Approximating solutions and their gradients in elliptic and parabolic problems on manifolds
Andrew D. Davis, Dimitrios Giannakis
We employ kernel-based approaches that use samples from a probability distribution to approximate a Kolmogorov operator on a manifold. The self-tuning variable-bandwidth kernel met…
Spectral analysis of climate dynamics with operator-theoretic approaches
Gary Froyland, Dimitrios Giannakis, Benjamin Lintner +2
The Earth's climate system is a classical example of a multiscale, multiphysics dynamical system with an extremely large number of active degrees of freedom, exhibiting variability…