Lyapunov analysis of data-driven models of high dimensional dynamics using reservoir computing: Lorenz-96 system and fluid flow

Abstract

We computed the Lyapunov spectrum and finite-time Lyapunov exponents of a data-driven model constructed using reservoir computing. This analysis was performed for two dynamics that exhibit a highly dimensionally unstable structure. We focused on the reconstruction of heterochaotic dynamics, which are characterized by the coexistence of different numbers of unstable dimensions. This was achieved by computing fluctuations in the number of positive finite-time Lyapunov exponents.

Keywords

• reservoir computing
• high-dimensional chaos
• Lyapunov exponents