Simple KS solver in JAX

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  • Опубліковано 14 чер 2024
  • 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

КОМЕНТАРІ • 12

  • @user-qp2ps1bk3b
    @user-qp2ps1bk3b 7 місяців тому +1

    very informative! Thank you

  •  7 місяців тому +1

    Well done. Thanks!

  • @vitorheitorcardosocunha3843
    @vitorheitorcardosocunha3843 7 місяців тому +1

    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
      @MachineLearningSimulation  5 місяців тому +1

      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
    @lineherz 22 дні тому

    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
      @thomassavary7075 21 день тому

      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
      @MachineLearningSimulation  7 днів тому

      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
    @amitnayak7917 7 місяців тому +1

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

    • @MachineLearningSimulation
      @MachineLearningSimulation  7 місяців тому

      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
      @nesslange1833 7 місяців тому

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