57 citations · 154 across the 18 of their papers we have counts for
9 papers · 1 filter
Learning Dynamical Systems with the Spectral Exterior Calculus
Suddhasattwa Das, Dimitrios Giannakis, Yanbing Gu +1
We present a data-driven framework for learning dynamical systems on compact Riemannian manifolds based on the spectral exterior calculus (SEC). This approach represents vector fie…
Quantum mechanical closure of partial differential equations with symmetries
Chris Vales, David C. Freeman, Joanna Slawinska +1
We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum…
Second quantization for classical nonlinear dynamics
Dimitrios Giannakis, Mohammad Javad Latifi Jebelli, Michael Montgomerry +3
Using techniques from many-body quantum theory, we propose a framework for representing the evolution of observables of measure-preserving ergodic flows through infinite-dimensiona…
Tensor network approximation of Koopman operators
Dimitrios Giannakis, Mohammad Javad Latifi Jebelli, Michael Montgomery +3
We propose a tensor network framework for approximating the evolution of observables of measure-preserving ergodic systems. Our approach is based on a spectrally-convergent approxi…
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…
Reproducing kernel Hilbert space compactification of unitary evolution groups
Dimitrios Giannakis, Suddhasattwa Das, Joanna Slawinska
A framework for coherent pattern extraction and prediction of observables of measure-preserving, ergodic dynamical systems with both atomic and continuous spectral components is de…
Spatiotemporal pattern extraction by spectral analysis of vector-valued observables
Dimitrios Giannakis, Abbas Ourmazd, Joanna Slawinska +1
We present a data-driven framework for extracting complex spatiotemporal patterns generated by ergodic dynamical systems. Our approach, called Vector-valued Spectral Analysis (VSA)…