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: github.com/Ceyron/machine-lea...
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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

[@user-qp2ps1bk3b]

very informative! Thank you

[@MachineLearningSimulation]

Glad you enjoyed it! 😊

Well done. Thanks!

[@MachineLearningSimulation]

Thanks for watching! 😊

[@vitorheitorcardosocunha3843]

Your videos are very didactic and entertaining. Thanks! Maybe you could implement the compressible Navier-Stokes-Korteweg model using the Exponential Time differencing method? Or in Fenics? The model is also stiff and is becoming more and more popular among numerical engineers!

[@MachineLearningSimulation]

Hi, thanks for the kind words and the video suggestion :). I am not very familiar with this model but will keep it on my list for future videos. I cannot guarantee that there will be a video, but never say never :).

[@lineherz]

Could you explain how you came up with the equation following the sentence "Then advance the state in time by..."? Is there any prerequisite to understand the derivation?

[@thomassavary7075]

ETD (Exponential Time Differencing) is a numerical method to solve stiff ODEs, you can have a look at indico.ictp.it/event/a08165/session/7/contribution/4/material/0/0.pdf to understand the idea behind this equation (slides 19 to 22).

[@MachineLearningSimulation]

Hi,
Thanks for the question 😊
Can you give me a time stamp for when I said that in the video? It's been some time since I uploaded it.

[@amitnayak7917]

could you do a tutorial on implementing the immersed boundary method for incompressible NS?

[@MachineLearningSimulation]

Hi,
that's an interesting topic, but I am not familiar with it. Maybe at some time there will be a video, but not in the near future. Hope you can understand 😊

[@nesslange1833]

I'd also love to see a series on BEM (Boundary Element Method) tackled by you. Hopefully in the far Future. Keep on moving.