Sensitivity analysis of chaotic systems
Limitations of current adjoint-based optimisation algorithms when applied to turbulent flows motivated work on the Least Square Shadowing method, that produces reliable sensitivities of time-averaged quantities to variations of system parameters. We have developed a highly efficient algorithm that makes the convergence rate of the Shadowing method almost independent of the size of the dynamical system and the length of the trajectory used to compute the time-average. Very recently, we applied shadowing for feedback control of chaotic systems. We have also coupled it with polynomial chaos expansion for uncertainty quantification of time-average quantities and their sensitivities when the system parameters follow a prescribed probability density function. This coupling resulted in a faster approach, named Shadowed Polynomial Chaos Expansion.
- Shawki K and Papadakis G. (2020) Feedback control of chaotic systems using multiple shooting shadowing and application to Kuramoto–Sivashinsky equation. Proc. Roy. Soc. A 476: 20200322.
- K.D. Kantarakias and G. Papadakis (2020), Application of generalized Polynomial Chaos for Quantification of uncertainties of time--averages and their sensitivities in chaotic systems, Algorithms, 13(4), 90 [invited submission].
- K.D. Kantarakias, K. Shawki, and G. Papadakis (2020) Uncertainty quantification of sensitivities of time-average quantities in chaotic systems, Physical Review E 101, 022223
- K. Shawki and G. Papadakis (2019) A preconditioned Multiple Shooting Shadowing algorithm for the sensitivity analysis of chaotic systems, Journal of Computational Physics, 398, 108861.