Interpretable and Equation-Free Response Theory for Complex Systems | Paper Citation Record

Observation 0c2a98b2-ec71-4406-81f8-c1852b579b87 · outbound

This paper cites 1982 Stochastic processes: Time evolution, symmetries and linear response.Physics Reports88, 207 – 319.

Interpretable and Equation-Free Response Theory for Complex Systems 1982 Stochastic processes: Time evolution, symmetries and linear response.Physics Reports88, 207 – 319

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This paper cites 2013 An update on the nonequilibrium linear response.New Journal of Physics15, 013004.

Interpretable and Equation-Free Response Theory for Complex Systems 2013 An update on the nonequilibrium linear response.New Journal of Physics15, 013004

Reference 2

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This paper cites 2019 On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems.Chaos29, 083132.

Interpretable and Equation-Free Response Theory for Complex Systems 2019 On the fluctuation-dissipation relation in non-equilibrium and non-Hamiltonian systems.Chaos29, 083132

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Observation af5341bc-53ff-4fc3-821e-aa70f3271ee4 · outbound

This paper cites 1966 The fluctuation-dissipation theorem.Reports on Progress in Physics29, 255–284.

Interpretable and Equation-Free Response Theory for Complex Systems 1966 The fluctuation-dissipation theorem.Reports on Progress in Physics29, 255–284

Reference 4

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Observation 5823efb3-688d-45b6-992e-17c8281555b6 · outbound

This paper cites 2010 A simple framework to justify linear response theory.Nonlinearity 23, 909–922.

Interpretable and Equation-Free Response Theory for Complex Systems 2010 A simple framework to justify linear response theory.Nonlinearity 23, 909–922

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This paper cites 2008 Fluctuation–dissipation: response theory in statistical physics.Physics reports461, 111–195.

Interpretable and Equation-Free Response Theory for Complex Systems 2008 Fluctuation–dissipation: response theory in statistical physics.Physics reports461, 111–195

Reference 6

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Observation 431fbc40-e11d-4b59-ab1b-a8e977a1f813 · outbound

This paper cites 2014Stochastic Processes and Applicationsvol.

Interpretable and Equation-Free Response Theory for Complex Systems 2014Stochastic Processes and Applicationsvol

Reference 7

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Reference 8

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Observation c26e5f3a-fc63-46db-8a1e-75c9acaf5897 · outbound

This paper cites 2009 A review of linear response theory for general differentiable dynamical systems.Nonlinearity22, 855–870.

Interpretable and Equation-Free Response Theory for Complex Systems 2009 A review of linear response theory for general differentiable dynamical systems.Nonlinearity22, 855–870

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This paper cites 2006 Banach spaces adapted to Anosov systems.Ergodic Theory and Dynamical Systems26, 189–217.

Interpretable and Equation-Free Response Theory for Complex Systems 2006 Banach spaces adapted to Anosov systems.Ergodic Theory and Dynamical Systems26, 189–217

Reference 10

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This paper cites 2014 Linear response, or else.Proceedings of the International Congress of Mathematicians-Seoul3, 525–545.

Interpretable and Equation-Free Response Theory for Complex Systems 2014 Linear response, or else.Proceedings of the International Congress of Mathematicians-Seoul3, 525–545

Reference 11

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This paper cites 2017 Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables.Nonlinearity30, 1204–1220.

Interpretable and Equation-Free Response Theory for Complex Systems 2017 Linear and fractional response for the SRB measure of smooth hyperbolic attractors and discontinuous observables.Nonlinearity30, 1204–1220

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Observation 6c5eb08b-5d97-4b5b-81cf-596628cb8ea6 · outbound

This paper cites 1998 Nonequilibrium statistical mechanics near equilibrium: computing higher- order terms.Nonlinearity11, 5–18.

Interpretable and Equation-Free Response Theory for Complex Systems 1998 Nonequilibrium statistical mechanics near equilibrium: computing higher- order terms.Nonlinearity11, 5–18

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This paper cites 2008 Response theory for equilibrium and non-equilibrium statistical mechanics: Causality and generalized kramers-kronig relations.Journal of Statistical Physics131, 543–558.

Interpretable and Equation-Free Response Theory for Complex Systems 2008 Response theory for equilibrium and non-equilibrium statistical mechanics: Causality and generalized kramers-kronig relations.Journal of Statistical Physics131, 543–558

Reference 14

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This paper cites 2009 Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system.J.

Interpretable and Equation-Free Response Theory for Complex Systems 2009 Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system.J

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Observation 445e8183-e1d7-4e21-a8fd-ed9f481ecf12 · outbound

This paper cites 2020 Ruelle-Pollicott Resonances of Stochastic Systems in Reduced State Space.

Interpretable and Equation-Free Response Theory for Complex Systems 2020 Ruelle-Pollicott Resonances of Stochastic Systems in Reduced State Space

Reference 16

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This paper cites 2022 On some aspects of the response to stochastic and deterministic forcings.Journal of Physics A: Mathematical and Theoretical55, 425002.

Interpretable and Equation-Free Response Theory for Complex Systems 2022 On some aspects of the response to stochastic and deterministic forcings.Journal of Physics A: Mathematical and Theoretical55, 425002

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This paper cites 2023 Theoretical tools for understanding the climate crisis from Hasselmann’s programme and beyond.Nature Reviews Physics.

Interpretable and Equation-Free Response Theory for Complex Systems 2023 Theoretical tools for understanding the climate crisis from Hasselmann’s programme and beyond.Nature Reviews Physics

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This paper cites 2005 Spectral Properties of Dynamical Systems, Model Reduction and Decompositions.Nonlinear Dynamics41, 309–325.

Interpretable and Equation-Free Response Theory for Complex Systems 2005 Spectral Properties of Dynamical Systems, Model Reduction and Decompositions.Nonlinear Dynamics41, 309–325

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Observation 6fc1cd62-b399-448a-b2b8-af6ba7c9b270 · outbound

This paper cites 2012 Applied Koopmanism.Chaos22, 047510, 33.

Interpretable and Equation-Free Response Theory for Complex Systems 2012 Applied Koopmanism.Chaos22, 047510, 33

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Observation cb9a99c0-4ed5-408c-8f8c-a7a1313aa839 · outbound

This paper cites 2016Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems.

Interpretable and Equation-Free Response Theory for Complex Systems 2016Dynamic Mode Decomposition: Data-Driven Modeling of Complex Systems

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This paper cites 2022Data-driven Science and Engineering: Machine Learning, Dynamical Systems, and Control.

Interpretable and Equation-Free Response Theory for Complex Systems 2022Data-driven Science and Engineering: Machine Learning, Dynamical Systems, and Control

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Observation db130f2f-fce4-44cc-99f9-68385bf7565c · outbound

This paper cites 2018 Data-driven model reduction and transfer operator approximation.J.

Interpretable and Equation-Free Response Theory for Complex Systems 2018 Data-driven model reduction and transfer operator approximation.J

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Observation 6f9cea0f-fac5-4ffe-9462-6c7b3ef40a0a · outbound

This paper cites 2024 Chapter 4 - The multiverse of dynamic mode decomposition algorithms.

Interpretable and Equation-Free Response Theory for Complex Systems 2024 Chapter 4 - The multiverse of dynamic mode decomposition algorithms

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This paper cites Bridging the Gap between Koopmanism and Response Theory: Using Natural Variability to Predict Forced Response.

Interpretable and Equation-Free Response Theory for Complex Systems Bridging the Gap between Koopmanism and Response Theory: Using Natural Variability to Predict Forced Response

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Observation bb645cb1-53f2-46a8-8923-bc57e2f53dce · outbound

This paper cites A General Framework for Linking Free and Forced Fluctuations via Koopmanism.

Interpretable and Equation-Free Response Theory for Complex Systems A General Framework for Linking Free and Forced Fluctuations via Koopmanism

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This paper cites 2024 Kolmogorov Modes and Linear Response of Jump- Diffusion Models: Applications to Stochastic Excitation of the ENSO Recharge Oscillator.

Interpretable and Equation-Free Response Theory for Complex Systems 2024 Kolmogorov Modes and Linear Response of Jump- Diffusion Models: Applications to Stochastic Excitation of the ENSO Recharge Oscillator

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Observation 8cdca588-a4af-4afe-a95b-3f7d119ff583 · outbound

This paper cites 1998Markov Chains.

Interpretable and Equation-Free Response Theory for Complex Systems 1998Markov Chains

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Observation 55629fd0-6b8f-479a-a564-95ad8a4fe9a2 · outbound

This paper cites 2000Introduction to Markov Chains.

Interpretable and Equation-Free Response Theory for Complex Systems 2000Introduction to Markov Chains

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Observation 0fc92d97-395e-4fab-a4cd-47996c73a4b7 · outbound

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Interpretable and Equation-Free Response Theory for Complex Systems 1970 Markov Partitions for Axiom A Diffeomorphisms.American Journal of Mathematics92, 725–747

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Observation 3220c42f-9d4d-4a0d-bd37-b3e409bc59b8 · outbound

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Interpretable and Equation-Free Response Theory for Complex Systems 2010 Markov Chains and Dynamical Systems: The Open System Point of View

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Observation 794a38a5-6951-4cbe-b0b8-38d28dfee066 · outbound

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Interpretable and Equation-Free Response Theory for Complex Systems 1960A Collection of Mathematical Problems

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Observation f4f28009-b5e5-4b54-b38d-abfb10e5180e · outbound

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Interpretable and Equation-Free Response Theory for Complex Systems 2000Positive Transfer Operators and Decay of Correlationsvol

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Observation d19db3a5-0fc0-46ae-b6df-f897d16152e3 · outbound

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Interpretable and Equation-Free Response Theory for Complex Systems 1998 Approximating physical invariant measures of mixing dynamical systems in higher dimensions.Nonlinear Analysis: Theory, Methods & Applications32, 831–860

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Observation d5241b56-15e2-485c-a5ef-ee5f5cec56b5 · outbound

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Interpretable and Equation-Free Response Theory for Complex Systems 2002 Finite approximations of Markov operators.Journal of Computational and Applied Mathematics147, 137–152

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Observation 2771073c-73dc-420d-9285-da562347a226 · outbound

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Interpretable and Equation-Free Response Theory for Complex Systems 1991 Voronoi diagrams—a survey of a fundamental geometric data structure.ACM Comput

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Interpretable and Equation-Free Response Theory for Complex Systems 1965 Cluster Analysis of Multivariate Data: Efficiency versus Interpretability of Classification.Biometrics21, 768–769

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Observation 833e043e-524f-4ef8-9447-3f045e799939 · outbound

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Interpretable and Equation-Free Response Theory for Complex Systems 1982 Least squares quantization in PCM.IEEE Transactions on Information Theory28, 129–137

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Interpretable and Equation-Free Response Theory for Complex Systems 2006 Equilibrium Free Energies from Nonequilibrium Metadynamics.Phys

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Interpretable and Equation-Free Response Theory for Complex Systems 2010 Everything you wanted to know about Markov State Models but were afraid to ask.Methods52, 99–105

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Interpretable and Equation-Free Response Theory for Complex Systems 2014An introduction to Markov State Models and their application to long timescale molecular simulation

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Interpretable and Equation-Free Response Theory for Complex Systems 2018 Markov State Models: From an Art to a Science.Journal of the American Chemical Society140, 2386–2396

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Interpretable and Equation-Free Response Theory for Complex Systems 2014 A Computational Method to Extract Macroscopic Variables and Their Dynamics in Multiscale Systems.SIAM Journal on Applied Dynamical Systems13, 1816–1846

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Observation 2864e3ee-cfc3-4d95-be0a-0087bf1e977a · outbound

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Interpretable and Equation-Free Response Theory for Complex Systems 2018 Transition Manifolds of Complex Metastable Systems.Journal of Nonlinear Science28, 471–512

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Interpretable and Equation-Free Response Theory for Complex Systems 1965 Transport, Collective Motion, and Brownian Motion.Progress of Theoretical Physics33, 423–455

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Interpretable and Equation-Free Response Theory for Complex Systems 1961 Memory Effects in Irreversible Thermodynamics.Physical Review124, 983– 992

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Interpretable and Equation-Free Response Theory for Complex Systems 2015 A new framework for extracting coarse-grained models from time series with multiscale structure.Journal of Computational Physics296, 314–

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Interpretable and Equation-Free Response Theory for Complex Systems 2015Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations

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Interpretable and Equation-Free Response Theory for Complex Systems 2021 Reduced-order models for coupled dynamical systems: Data-driven methods and the Koopman operator.Chaos31, 053116

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Interpretable and Equation-Free Response Theory for Complex Systems 2021 Stochastic rectification of fast oscillations on slow manifold closures.Proc

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Resolution: verified exact; doi, observed 2026-08-08T11:32:56.199203Z

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Interpretable and Equation-Free Response Theory for Complex Systems 2025 Non-Markovian reduced models to unravel transitions in non-equilibrium systems.Journal of Physics A: Mathematical and Theoretical58, 045204

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Resolution: verified exact; doi, observed 2026-08-08T11:32:56.183683Z

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Interpretable and Equation-Free Response Theory for Complex Systems 2003 Equation-Free, Coarse-Grained Multiscale Computation: Enabling Macroscopic Simulators to Perform System-Level Analysis.Communications in Mathematical Sciences1, 718–762

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Interpretable and Equation-Free Response Theory for Complex Systems Drone-Based Antenna Measurement System with Optimized Positioning and ASPIRE-Based NF-FF Transformation

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Observation 482362db-18b3-47df-9b48-c5b03d580c8d · outbound

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