Global ETD Search
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Showing 1 to 15 of 15 for “"chaotic dynamical systems"”.
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Neural Closure Models for Chaotic Dynamical Systems
… prediction and ocean modeling, is that these dynamical systems are chaotic in nature. A hallmark of chaotic dynamical systems is that they are highly sensitive to small perturbations in the initial conditions and parameter values. As a result, even the best physics-based computational models, …
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Modeling and control of evolving, noisy chaotic dynamical systems
We study the modeling and control of evolving dynamical systems. In particular we model the dynamics of an evolving noisy iterative map, we study the extraction of the control parameter of the same map using a sparse time series from it, and we also study the dynamics of an evolving electronic …
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New methods for sensitivity analysis of chaotic dynamical systems
… when applied to long-time averaged quantities in chaotic dynamical systems, such as those obtained from high-fidelity turbulence simulations. Also, a number of dynamical properties of chaotic systems, most notably the "Butterfly Effect", make the formulation of new sensitivity analysis methods …
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Characterisation of local properties and prediction in chaotic dynamical systems
… in state space of conservative and dissipative chaotic systems that allow statements about future states or the predictability. This is done using two kinds of local exponents as well as ensemble studies. In conservative systems with trapping, the distribution of finite-time Lyapunov exponents …
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Least Squares Shadowing for sensitivity analysis of chaotic dynamical systems
In numerous scientific and engineering fields, sensitivity analysis tools are essential for design optimization as well as uncertainty quantification. For instance, adjoint algorithms are common place in aerospace engineering when it comes to optimize the shape of an airfoil, the configuration of a …
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Regular sensitivity calculation and gradient-based optimization of chaotic dynamical systems
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2023-12-01
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Statistical self-similarity in time series from financial data & chaotic dynamical systems
In this paper, I am going to introduce statistical self-similarity for discrete time series. My thesis is divided into three parts:
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Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS)
… sensitivity for long-time averaged objectives in chaotic dynamical systems. In NILSS, we represent a tangent solution by a linear combination of one inhomogeneous tangent solution and several homogeneous tangent solutions. Next, we solve a least squares problem using this representation; thus, the …
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Leveraging the Linear Response Theory in Sensitivity Analysis of Chaotic Dynamical Systems and Turbulent Flows
… derivatives of observables induced by a dynamical system. These derivatives, usually referred to as sensitivities, are critical components of optimization, control, numerical error estimation, risk assessment and other advanced computational methodologies. Efficient computation of …
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Framework for the analysis and design of encryption strategies based on discrete-time chaotic dynamical systems
Since 1990s chaotic dynamical systems have been widely used to design new strategies to encrypt information. Indeed, the dependency to initial conditions and control parameters, along with the ergodicity of their temporal evolution allow the establishment of chaos as the base of new cryptosystems, …
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Stationary Density Computation of the Frobenius-Perron Operators Based on the Dirac Delta Function
<p>The statistical study of chaotic dynamical systems has received a great deal of attention in the past several decades. As a branch of applied mathematics, its application has been found in various fields in science and engineering, while the theory and methods for the existence and computation …
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Rigidity results for thermostats
A thermostat is a dynamical system modelling the motion of a particle on a surface under the influence of a force that is always orthogonal to its velocity. Since this force is allowed to depend on the particle's velocity, the system can be dissipative. As a generalization of geodesic and magnetic …
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Microscopic Chaos, Fractals, and Transport in Nonequilibrium Steady States. - (Die Veröffentlichung einer ergänzten und überarbeiteten Version bei "World Scientific Publishing" ist für 2005/06 geplant.)
… transport: One considers Hamiltonian dynamical systems under nonequilibrium boundary conditions, another one suggests a non-Hamiltonian approach to nonequilibrium situations created by external electric fields and by temperature or velocity gradients. A surprising result related to the …
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Historical Consistent Neural Networks for Wind Power Prediction
Modeling chaotic dynamical systems remains a fundamental challenge due to their inherent non-linearity, sensitivity to initial conditions, and long-range temporal dependencies. While Recurrent Neural Networks (RNNs) are widely used for such tasks, they often suffer from temporal inconsistency: …