Full Lyapunov Spectrum of Chaotic Lorenz System using JAX скачать в хорошем качестве

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... --- 👉 This educational series is supported by the world-leaders in integrating machine learning and artificial intelligence with simulation and scientific computing, Pasteur Labs and Institute for Simulation Intelligence. Check out https://simulation.science/ for more on their pursuit of 'Nobel-Turing' technologies (https://arxiv.org/abs/2112.03235 ), and for partnership or career opportunities. ------- 📝 : Check out the GitHub Repository of the channel, where I upload all the handwritten notes and source-code files: https://github.com/Ceyron/machine-lea... 📢 : Follow me on LinkedIn or Twitter for updates on the channel and other cool Machine Learning & Simulation stuff:   / felix-koehler   and   / felix_m_koehler   💸 : If you want to support my work on the channel, you can become a Patreon here:   / mlsim   🪙: Or you can make a one-time donation via PayPal: https://www.paypal.com/paypalme/Felix... --- 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