Probability density adjoint for sensitivity analysis of the Mean of Chaos
Author(s)Blonigan, Patrick Joseph; Wang, Qiqi
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Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. This paper presents a new method for sensitivity analysis of ergodic chaotic dynamical systems, the density adjoint method. The method involves solving the governing equations for the system's invariant measure and its adjoint on the system's attractor manifold rather than in phase-space. This new approach is derived for and demonstrated on one-dimensional chaotic maps and the three-dimensional Lorenz system. It is found that the density adjoint computes very finely detailed adjoint distributions and accurate sensitivities, but suffers from large computational costs.
DepartmentMassachusetts Institute of Technology. Department of Aeronautics and Astronautics
Journal of Computational Physics
Blonigan, Patrick J., and Qiqi Wang. “Probability Density Adjoint for Sensitivity Analysis of the Mean of Chaos.” Journal of Computational Physics 270 (August 2014): 660–686.