Project Ideas for Google's Summer of Code

[JonathanWenger]

This thread collects project ideas for Google's summer of code.

BVP solvers and state-space optimisers.

Basically, implement https://arxiv.org/abs/2106.07761. This would make a counterpart of https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_bvp.html. The very basics should be pretty simple to build (all parts are there), but getting it right will take the student a bit, I guess. Perhaps easy to combine with probabilistic-numerics/probnum#248.

Linear Algebra / Galerkin methods

All of the below should be done in the autodiff backend:

• implement commonly used preconditioners
  • Jacobi
  • incomplete Cholesky
  • SPAI
  • for GPs (Nyström, RFF, QFF, NNGP?)
• implement sparse linear operators
• benchmark the probabilistic linear solver and implement a lazy version

[luffingluffy]

@JonathanWenger @pnkraemer Hello Jonathan and Kraemer, I am interested in contributing towards ProbNum and I have submitted a proposal for GSOC's 2022. I am still waiting on the outcome for that however, I would still like to contribute regardless of whether I'm accepted. I've taken a look at the website and tried using some of the features as well as looked at the Github code a little and I would like to try working on contributing towards a feature.

Furthermore, I understand that ProbNum relies on JAX's autodiff so I will take a look at that however, is there anything which you can recommend me to work towards as well as further resources which I can refer to?

[JonathanWenger]

Hi @luffingluffy sorry for the delayed response, I only had limited availability over the summer. If you're still interested in contributing let me know! Then we can talk about what makes the most sense.

[luffingluffy]

Hi, @JonathanWenger no worries and yep, I am still interested in contributing :)

[JonathanWenger]

Awesome. One feature that would be useful is to have a set of preconditioners available to quickly solve linear systems. Most prominently the Jacobi and incomplete Cholesky preconditioners. These could live under probnum/linalg/preconditioners and should inherit from LinearOperator. if that's a project you are interested in, let me know. Otherwise there are always open issues you could scan through to find a topic you are interested in and I'd be happy to give additional input.

[luffingluffy]

That sounds interesting, I don’t mind working on it!