Forward and Adjoint Sensitivity Computation of Chaotic Dynamical Systems

Abstract

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. The algorithms are demonstrated on the Lorenz attractor. We show that sensitivity derivatives of statistical quantities can be accurately estimated using a single, short trajectory (over a time interval of 20) on the Lorenz attractor.

3/7/2012: applied chain rule to Equation (7), so that Equations (15), (16) and (17) go through w.o. differentiable Lyapunov vectors. = 4/10/2012: Windowing scheme for forward sensitivity. Reduced heavy-tailedness in computed derivatives. Updated Figs 8 and 9. = 9/7/2012: Minor revision, accepted by JCP

References in corpus (2)

• Characterizing dynamics with covariant Lyapunov vectors
• A review of linear response theory for general differentiable dynamical systems

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