A tutorial for integrating ODEs multiple times

[A2P2]

Hi,
I'm wondering if there is a need to contribute with a tutorial for integrating ODEs multiple times based on different initial conditions. It's also possible to extend the current Lotka-Volterra example instead.

I oriented myself about the usage of jax.vmap for this purpose with the help of forums:
https://forum.pyro.ai/t/parallelization-plate-and-odes/2763
https://forum.pyro.ai/t/making-a-for-loop-more-efficient/3437/22

Is it of interest? Let me know what you think.

[fehiepsi]

The contribution would be awesome! Currently, we only have an example for Lotka-Volterra. A tutorial with motivations for your usage case would be super helpful for users.

[zz100chan]

@A2P2 hi! I think this is a good contribution and I am also somewhat have similar issues now.
I wonder if you have a tutorial already? :)

[A2P2]

@zz100chan
My apologies for the late reply and for generally ignoring the thread.

I do have a draft written, see it attached. I tried to follow the style of the current Lotka-Volterra tutorial. Let me know if it works for you and if something is not clear. Once again, it's in a draft state at the moment. Attached as a zip file.

lotka_volterra_multiple.zip

I've tried to implement a few things: 1) integrate with different initial conditions, 2) allowed to have missing values in the data. I use regularly spaced time arrays, but it's not a must.

The MCMC is somewhat slow. I've turned on numpyro.enable_x64(), otherwise problems with convergence were observed. For my job, I actually used solvers from the https://github.com/patrick-kidger/diffrax package instead of ones from jax, due to some convergence problems as well.

@fehiepsi I'm glad to finish the tutorial properly if you provide some feedback. Once again, my apologies for disappearing.

[fehiepsi]

Could you make a version of it on https://gist.github.com/?

[A2P2]

@fehiepsi here you are https://gist.github.com/A2P2/5d2b3a15eafd5e0857ed1c49e4c1b1f4

[fehiepsi]

Thank you! I'll take a look later of the week.

[fehiepsi]

Hi @A2P2, the example looks great. In the tutorial, it would be nice to include some introduction to the model, how the dataset looks like, and motivation for integrating ODEs multiple times.

[A2P2]

@fehiepsi thanks for checking it quickly. I've added a short motivation to the gist, I'll add the dataset description later.
Shall I make a pull request with it?

[fehiepsi]

Could you turn it into a (probably short?) tutorial, rather than an example? We have several tutorials here (those without Example: prefix).

[A2P2]

Will do!

[A2P2]

@fehiepsi here is the tutorial version on colab, let me know what you think.
https://gist.github.com/A2P2/ae09ed99f84372ff346b0d352ca7b4ed

[fehiepsi]

super cool, @A2P2 !