Adjoint sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Adjoint Shadowing (NILSAS)

Abstract

We develop the NILSAS algorithm, which performs adjoint sensitivity analysis of chaotic systems via computing the adjoint shadowing direction. NILSAS constrains its minimization to the adjoint unstable subspace, and can be implemented with little modification to existing adjoint solvers. The computational cost of NILSAS is independent of the number of parameters. We demonstrate NILSAS on the Lorenz 63 system and a weakly turbulent three-dimensional flow over a cylinder.

34 pages, 11 figures. The adjoint shadowing direction which we compute is defined at arXiv:1807.05568

References in corpus (7)

• Hyperbolicity, shadowing directions and sensitivity analysis of a turbulent three-dimensional flow
• Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models
• Sensitivity analysis on chaotic dynamical systems by Finite Difference Non-Intrusive Least Squares Shadowing (FD-NILSS)
• Lyapunov spectrum of separated flows and its dependence on numerical discretization
• Toward a chaotic adjoint for LES
• Adjoint shadowing directions in hyperbolic systems for sensitivity analysis
• Linear Range in Gradient Descent

Cited by in corpus (8)

• Gradient-free optimization of chaotic acoustics with reservoir computing
• Sensitivity analysis on chaotic dynamical systems by Finite Difference Non-Intrusive Least Squares Shadowing (FD-NILSS)
• Sensitivity analysis of chaotic systems using a frequency-domain shadowing approach
• Recursive divergence formulas for perturbing unstable transfer operators and physical measures
• Adjoint shadowing directions in hyperbolic systems for sensitivity analysis
• Variational optimization and data assimilation in chaotic time-delayed systems with automatic-differentiated shadowing sensitivity
• Approximating linear response by nonintrusive shadowing algorithms
• Fast differentiation of hyperbolic chaos