Least Squares Shadowing Sensitivity Analysis of a Modified Kuramoto-Sivashinsky Equation

Abstract

Computational methods for sensitivity analysis are invaluable tools for scientists and engineers investigating a wide range of physical phenomena. However, many of these methods fail when applied to chaotic systems, such as the Kuramoto-Sivashinsky (K-S) equation, which models a number of different chaotic systems found in nature. The following paper discusses the application of a new sensitivity analysis method developed by the authors to a modified K-S equation. We find that least squares shadowing sensitivity analysis computes accurate gradients for solutions corresponding to a wide range of system parameters.

23 pages, 14 figures. Submitted to Chaos, Solitons and Fractals, in review

References in corpus (2)

• Convergence of the least squares shadowing method for computing derivative of ergodic averages
• Probability density adjoint for sensitivity analysis of the Mean of Chaos

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• Sensitivity Analysis of Chaotic Systems using Unstable Periodic Orbits
• Stability, sensitivity and optimisation of chaotic acoustic oscillations
• Periodic Shadowing Sensitivity Analysis of Chaotic Systems
• On the probability of finding a nonphysical solution through shadowing
• Computational assessment of smooth and rough parameter dependence of statistics in chaotic dynamical systems
• A Preconditioned Multiple Shooting Shadowing Algorithm for the Sensitivity Analysis of Chaotic Systems
• Least Squares Shadowing for Sensitivity Analysis of Turbulent Fluid Flows
• Sensitivity analysis of chaotic systems using a frequency-domain shadowing approach
• Approximating linear response by nonintrusive shadowing algorithms
• Space-split algorithm for sensitivity analysis of discrete chaotic systems with unstable manifolds of arbitrary dimension
• Sensitivity computation of statistically stationary quantities in turbulent flows