Forward and adjoint sensitivity computation of chaotic dynamical systems

Journal Article · Fri Feb 15 00:00:00 EST 2013 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2012.09.007· OSTI ID:22233554

Wang, Qiqi ^[1]

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1. Department of Aeronautics and Astronautics, MIT, 77 Mass Ave., Cambridge, MA 02139 (United States)

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.

• OSTI ID: 22233554
• Journal Information: Journal of Computational Physics, Vol. 235; Other Information: Copyright (c) 2012 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
ALGORITHMS
ATTRACTORS
CHAOS THEORY
DISTURBANCES
EQUATIONS
LYAPUNOV METHOD
PERTURBATION THEORY
SENSITIVITY ANALYSIS
VECTORS