Largest Lyapunov Exponent using Autodiff in JAX/Python скачать в хорошем качестве

Largest Lyapunov Exponent using Autodiff in JAX/Python

Let's approximate the largest Lyapunov exponent of the Lorenz System by evolving a perturbation using the tangent linear dynamics of an RK4 simulator with a Jacobian-vector product (forward-mode AD) in JAX. 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 01:00 Approach for this video 01:58 Algorithm Overview 05:17 Recap: RK4 Lorenz Simulator in JAX 06:19 Evolve a perturbation next to the trajectory integration 12:11 Warm up initial state 12:53 Produce growth trajectory 14:47 Approximate largest Lyapunov Exponent 16:33 Investigate convergence behavior of Lyapunov approximation 23:02 Improving the approximation 24:46 Avoid instantiating the dense Jacobian with jax.jvp 29:03 Outro