57 citations · 154 across the 18 of their papers we have counts for
18 papers
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…
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…
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…
Embedding classical dynamics in a quantum computer
Dimitrios Giannakis, Abbas Ourmazd, Philipp Pfeffer +2
We develop a framework for simulating measure-preserving, ergodic dynamical systems on a quantum computer. Our approach provides a new operator-theoretic representation of classica…
Extended-range statistical ENSO prediction through operator-theoretic techniques for nonlinear dynamics
Xinyang Wang, Joanna Slawinska, Dimitrios Giannakis
Forecasting the El Nino-Southern Oscillation (ENSO) has been a subject of vigorous research due to the important role of the phenomenon in climate dynamics and its worldwide socioe…
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…
The Antarctic circumpolar wave and its seasonality: Intrinsic traveling modes and ENSO teleconnections
Xinyang Wang, Dimitrios Giannakis, Joanna Slawinska
Interannual variability in the Southern Ocean is investigated via nonlinear Laplacian spectral analysis (NLSA), an objective eigendecomposition technique for nonlinear dynamical sy…
Vector-Valued Spectral Analysis of Space-Time Data
Dimitrios Giannakis, Joanna Slawinska, Abbas Ourmazd +1
Identifying coherent spatiotemporal patterns generated by complex dynamical systems is a central problem in many science and engineering disciplines. Here, we combine ideas from th…
Data-Driven Koopman Analysis of Tropical Climate Space-Time Variability
Joanna Slawinska, Eniko Szekely, Dimitrios Giannakis
We study nonlinear dynamics of the Earth's tropical climate system. For that, we apply a recently developed technique for feature extraction and mode decomposition of spatiotempora…
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)…
Indo-Pacific variability on seasonal to multidecadal timescales. Part II: Multiscale atmosphere-ocean linkages
Dimitrios Giannakis, Joanna Slawinska
The coupled atmosphere-ocean variability of the Indo-Pacific on interannual to multidecadal timescales is investigated in a millennial control run of CCSM4 and in observations usin…
Indo-Pacific variability on seasonal to multidecadal timescales. Part I: Intrinsic SST modes in models and observations
Joanna Slawinska, Dimitrios Giannakis
The variability of Indo-Pacific SST on seasonal to multidecadal timescales is investigated using a recently introduced technique called nonlinear Laplacian spectral analysis (NLSA)…