Simple KS solver in JAX

The Kuramoto-Sivashinsky is a fourth-order partial differential equation that shows highly chaotic dynamics. It has become an exciting testbed for deep learning methods in physics. Here, we will code a simple Exponential Time Differencing (ETD) solver in JAX/Python. Code: https://github.com/Ceyron/machine-learning-and-simulation/blob/main/english/fft_and_spectral_methods/ks_solver_etd_in_jax.ipynb

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Timestamps:
00:00 Intro
01:10 Exponential Time Differencing Methods & Spectral Derivatives
02:26 Domain Size as a crucial parameter
02:42 Here: the "Euler" ETD method
03:22 Simulation Algorithm for the KS equation
07:09 Imports & Constants
08:01 KS integrator class Constructor
12:19 KS integrator class Call method
15:11 Mesh & Initial Condition
16:29 Plot IC & first steps
17:40 Produce trajectory by autoregressive rollout
19:10 Visualize spatiotemporal plot
21:20 Summary
22:33 Outro

Видео Simple KS solver in JAX канала Machine Learning & Simulation