patrick-kidger / patrick-kidger/diffrax

Implementation of multirate methods in diffrax

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Description

Has there been discussion of implementing multirate methods in diffrax? See Sec. 2.4.3. of the linked article, Fig. 4.

By this, I mean methods tailored to the case where ODETerm has components that have an explicit separation in timescales, such that different time steps can be used internally when solving for the separated components.

My understanding is that the IMEX methods partly address this but wash out the fast component in favor of an accurate slow component (adiabatic elimination). I am thinking of multirate methods which accurately capture both the fast and slow components.

If my above understanding is not correct, feel free to educate me.

I think multirate methods could be a valuable tool in a wide array of physics problems. I would like to know how other people feel about this.

Contributor guide

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First steps

  1. Read the whole issue, then the project's contributing guide.
  2. Comment on the issue to say you are picking it up — it saves two people doing the same work.
  3. Fork the repository and make your change on a branch.
  4. Open a pull request that references the issue number.

Research direction

Start by reading Sec. 2.4.3 and Fig. 4 of the linked article, then inspect how diffrax represents an ODETerm and its existing IMEX methods. The issue names no source files or tests; progress would first require agreeing on the multirate scope, expected behavior for fast and slow components, and validation criteria.

Written by the indexing model from the issue text.

Assessment

Tech stack
python
Domain
backend
Issue type
Feature
Difficulty
5/5
Estimated time
Over a week
Activity status
Stale
Clarity
Needs clarification
Newbie friendliness
25/100

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