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Nonintrusive shadowing algorithms efficiently compute $v$, the difference between shadowing trajectories, then use $v$ to compute derivatives of averaged objectives of chaos with respect to parameters of the dynamical system.
Geodesic flows on closed Riemannian manifolds of negative curvature
D. V. Anosov · 1967
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Markov Partitions for Axiom A Diffeomorphisms
R. Bowen · 1970
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Gibbs Measures in Ergodic Theory
Y. G. Sinai · 1972
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The ergodic theory of Axiom A flows
R. Bowen and D. Ruelle · 1975
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A Measure Associated with Axiom-A Attractors
D. Ruelle · 1976
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Decay of correlations in certain hyperbolic systems
G. Casati, G. Comparin, and I. Guarneri · 1982
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Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem
G. Gallavotti · 1996
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Shadowing in Structurally Stable Flows
S. Y. Pilyugin · 1997
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Differentiation of SRB States
D. Ruelle · 1997
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Sensitivity analysis of the climate of a chaotic system
D. J. Lea, M. R. Allen, and T. W. N. Haine · 2000
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What are SRB measures, and which dynamical systems have them?
L.-S. Young · 2002
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Differentiation of SRB States: Correction and Complements
D. Ruelle · 2003
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On differentiability of SRB states for partially hyperbolic systems
D. Dolgopyat · 2004
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Ruelle’s linear response formula, ensemble adjoint schemes and Lévy flights
G. L. Eyink, T. W. N. Haine, and D. J. Lea · 2004
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Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems
R. V. Abramov and A. J. Majda · 2007
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New Approximations and Tests of Linear Fluctuation-Response for Chaotic Nonlinear Forced-Dissipative Dynamical Systems
R. V. Abramov and A. J. Majda · 2008
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Differentiation of SRB states for hyperbolic flows
D. Ruelle · 2008
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Differentiating potential functions of SRB measures on hyperbolic attractors
M. Jiang · 2012
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Linear response, or else
V. Baladi · 2014
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Least squares shadowing sensitivity analysis of a modified Kuramoto-Sivashinsky equation
P. J. Blonigan and Q. Wang · 2014
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An elementary approach to rigorous approximation of invariant measures
S. Galatolo and I. Nisoli · 2014
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Convergence of the Least Squares Shadowing Method for Computing Derivative of Ergodic Averages
Q. Wang · 2014
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Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS)
A. Ni and Q. Wang · 2017
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A rigorous computational approach to linear response
W. Bahsoun, S. Galatolo, I. Nisoli, and X. Niu · 2018
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Multiple shooting shadowing for sensitivity analysis of chaotic dynamical systems
P. J. Blonigan and Q. Wang · 2018
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Algorithmic differentiation of shadowing sensitivities in chaotic systems
N. Chandramoorthy, Q. Wang, L. Magri, S. H. K. Narayanan, and P. Hovland · 2018
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Adjoint shadowing directions in hyperbolic systems for sensitivity analysis
A. Ni · 2018
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Fluctuations of Observables in Dynamical Systems: From Limit Theorems to Concentration Inequalities
J.-R. Chazottes · 2015
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Least Squares Shadowing for Sensitivity Analysis of Large Chaotic Systems and Fluid Flows
P. J. Blonigan · 2016
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Rigorous computation of invariant measures and fractal dimension for maps with contracting fibers: 2D Lorenz-like maps
S. Galatolo and I. Nisoli · 2016
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Adjoint sensitivity analysis of chaotic dynamical systems with non-intrusive least squares shadowing
P. J. Blonigan · 2017
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An Analysis of the Ensemble Adjoint Approach to Sensitivity Analysis in Chaotic Systems
N. Chandramoorthy, P. Fernandez, C. Talnikar, and Q. Wang · 2017
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Least Squares Shadowing Method for Sensitivity Analysis of Differential Equations
M. Chater, A. Ni, P. J. Blonigan, and Q. Wang · 2017
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Y. S. Shimizu and K. J. Fidkowski · 2018
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Periodic shadowing sensitivity analysis of chaotic systems
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Hyperbolicity, shadowing directions and sensitivity analysis of a turbulent three-dimensional flow
A. Ni · 2019
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Adjoint sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Adjoint Shadowing (NILSAS)
A. Ni and C. Talnikar · 2019
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Sensitivity analysis on chaotic dynamical systems by Finite Difference Non-Intrusive Least Squares Shadowing (FD-NILSS)
A. Ni, Q. Wang, P. Fernandez, and C. Talnikar · 2019
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A preconditioned multiple shooting shadowing algorithm for the sensitivity analysis of chaotic systems
K. Shawki and G. Papadakis · 2019
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Fourier approximation of the statistical properties of Anosov maps on tori
H. Crimmins and G. Froyland · 2020
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Fast linear response algorithm for differentiating chaos
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Using the LSS adjoint for simultaneous plant and control optimization of chaotic dynamical systems
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