Forward and Adjoint Sensitivity Computation of Chaotic Dynamical Systems

Details Forward and Adjoint Sensitivity Computation of Chaotic Dynamical Systems Forward and Adjoint Sensitivity Computation of Chaotic Dynamical Systems

2012-02-23

arxiv.org/abs/1202.5229v3

Physics

Computational Physics

3/7/2012: Added equation numbers for (10) and (11); applied chain rule to Equation (7), so that the arguments in Equations (15

Scientific paper

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.

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