Full Lyapunov Spectrum of Chaotic Lorenz System using JAX

The largest Lyapunov exponent indicates the presence of deterministic chaos in a dynamical system. Additionally, more interesting properties of a system can be deduced from an entire Lyapunov spectrum, e.g., the Kaplan-Yorke dimension describing the fractal structure. Let's approximate the full spectrum via pushing orthonormal matrix variations through the integration on the chaotic attractor. We will derive the integrator's Jacobian using JAX's automatic differentiation engine. Here is the code: https://github.com/Ceyron/machine-lea...

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Timestamps:
00:00 Intro
00:33 Deterministic Chaos (& largest Lyapunov exponent)
00:57 The Lyapunov Spectrum
01:49 Algorithm Overview
05:29 Simulator Recap
06:26 Implement Orthonormal Matrix Integrator
12:20 Initial perturbation matrix
12:57 Produce growth trajectory
13:46 Approximate Lyapunov Spectrum from growth trajectory
14:44 Rescale to correct dt
15:30 Discussing the Lyapunov Spectrum
17:23 Improved Jacobian multiplication via JAX tricks
21:34 Outro