Lorenz Simulator in NumPy

The Lorenz attractor is a system of nonlinear ODEs serving as the prototypical example of deterministic chaos. Let's simulate it with a Rung-Kutta 4 scheme and visualizes its 3D butterfly shape. Here is the code: https://github.com/Ceyron/machine-learning-and-simulation/blob/main/english/simulation_scripts/lorenz_simulator_numpy.ipynb ------- 👉 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-learning-and-simulation 📢 : Follow me on LinkedIn or Twitter for updates on the channel and other cool Machine Learning & Simulation stuff: https://www.linkedin.com/in/felix-koehler and https://twitter.com/felix_m_koehler 💸 : If you want to support my work on the channel, you can become a Patreon here: https://www.patreon.com/MLsim 🪙: Or you can make a one-time donation via PayPal: https://www.paypal.com/paypalme/FelixMKoehler ----- Timestamps: 00:00 Intro 01:33 How we are going to do it 02:07 About the Runge-Kutta (RK4) scheme 03:03 Implementing the right-hand side of Lorenz system 04:50 Implementing Autoregressive TimeStepper 10:18 Integrate Trajectory 12:55 Visualization 16:35 Discussion 17:40 Outro