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Neural Closure Models for Chaotic Dynamical Systems
Published 2023“…A hallmark of chaotic dynamical systems is that they are highly sensitive to small perturbations in the initial conditions and parameter values. …”
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Multigrid-in-time for sensitivity analysis of chaotic dynamical systems
Published 2017“…The following paper discusses the application of a multigrid-in-time scheme to Least Squares Shadowing (LSS), a novel sensitivity analysis method for chaotic dynamical systems. While traditional sensitivity analysis methods break down for chaotic dynamical systems, LSS is able to compute accurate gradients. …”
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Efficient Bayesian inference for large chaotic dynamical systems
Published 2022“…We perform Bayesian inference of parameters in high-dimensional and computationally demanding chaotic dynamical systems by combining two approaches: (i) measuring model–data mismatch by comparing chaotic attractors and (ii) mitigating the computational cost of inference by using surrogate models. …”
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New methods for sensitivity analysis of chaotic dynamical systems
Published 2013Get full text
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Forward and adjoint sensitivity computation of chaotic dynamical systems
Published 2015“…This paper describes a forward algorithm and an adjoint algorithm for computing sensitivity derivatives in chaotic dynamical systems, such as the Lorenz attractor. The algorithms compute the derivative of long time averaged “statistical” quantities to infinitesimal perturbations of the system parameters. …”
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A First Course In Chaotic Dynamical Systems : Theory And Experiment /
Published 2020“…The area of dynamical systems covered in A First Course in Chaotic Dynamical Systems: Theory and Experiment, Second Edition is quite accessible to students and also offers a wide variety of interesting open questions for students at the undergraduate level to pursue. …”
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Least Squares Shadowing for sensitivity analysis of chaotic dynamical systems
Published 2016Get full text
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Multiple shooting shadowing for sensitivity analysis of chaotic dynamical systems
Published 2021“…Unfortunately, conventional sensitivity analysis methods are unable to compute useful gradient information for long-time-averaged quantities in chaotic dynamical systems. Sensitivity analysis with least squares shadowing (LSS) can compute useful gradient information for a number of chaotic systems, including simulations of chaotic vortex shedding and homogeneous isotropic turbulence. …”
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Blended particle filters for large-dimensional chaotic dynamical systems
Published 2014“…Thus, a major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. New blended particle filters are developed in this paper. …”
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Adaptive control scheme for anti- synchronization of chaotic dynamical systems
Published 2016“…Due to physical limitation in most real-world applications, the assumption on chaotic dynamical systems with identical drive and response systems is somehow unrealistic. …”
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Scaling Analysis of an Image Encryption Scheme Based on Chaotic Dynamical Systems
Published 2021-05-01Get full text
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Comparison of Feedforward and Recurrent Neural Network in Forecasting Chaotic Dynamical System
Published 2019-04-01Get full text
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Generalized synchronization of identical and nonidentical chaotic dynamical systems via master approaches
Published 2017-10-01Get full text
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Interpretable predictions of chaotic dynamical systems using dynamical system deep learning
Published 2024-02-01“…Abstract Making accurate predictions of chaotic dynamical systems is an essential but challenging task with many practical applications in various disciplines. …”
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