Interpolation of 2d data

[TorkelE]

Is this possible? And if so, would I be able to combine it with https://docs.sciml.ai/ModelingToolkit/stable/tutorials/callable_params/?

[SouthEndMusic]

DataInterpolations.jl is built from the ground up with 1D interpolation in mind, you could look into using Bsplines for instance

[ChrisRackauckas]

We could start going into multidimensional interpolations, but we just haven't yet. 1D had a lot of work and I feel like we're finally getting to the conclusion there, maybe this summer is the right time to start expanding but it would need more hands maybe.

[TorkelE]

Sounds good.

(I was writing tests and tutorials for doing this kind of stuff in Catalyst, and was thinking that if 2d existed I'd add that in as well, but will keep it at 1d then. Feel free to close/keep open this issue as you like)

[SouthEndMusic]

To clarify, I'd be happy to contribute to 2d interpolation if I find the time, I assumed it would be outside the scope of this package.

I wrote the package SplineGrids.jl a few months ago for n-dimensional interpolation (with evaluation on a grid), maybe we can take inspiration from that.

[ChrisRackauckas]

If you already have a starting point then we should just start there. I think the main thing is that we just needs to make sure it has all of the integrations (AD, MTK, etc.) that people expect. It's fine for it to be a separate repo but we just need to have a direction for that work. Indeed 1D vs ND can be quite different in form so separate repo might be the right thing to do, but Interpolations.jl just isn't sufficient for most people so we do need to take it into our own hands in the very near future.

[SouthEndMusic]

To get some sense of goal/scope:

1. is the domain always a (hyper)rectangle and the input data structured in arrays?
2. Is interpolation in all dimensions the same or should interpolation types be mixable?
3. SplineGrids.jl is built on KernelAbstractions.jl, is that a good fit? GPU support is nice
4. There's probably already quite a lot of work done in other packages for interpolations on spatial discretizatons for PDEs, so do we want to cater for that, or is this targeted at very different things?

[ChrisRackauckas]

is the domain always a (hyper)rectangle and the input data structured in arrays?

Yes

Is interpolation in all dimensions the same or should interpolation types be mixable?

I think all dimensions the same?

SplineGrids.jl is built on KernelAbstractions.jl, is that a good fit? GPU support is nice

Yes. And if GPU support, possibility to use texture memory? That would be a massive performance win.

There's probably already quite a lot of work done in other packages for interpolations on spatial discretizatons for PDEs, so do we want to cater for that, or is this targeted at very different things?

Semi-discretizations are very different. This is more for data tables, f(x,y,z) -> value

[sathvikbhagavan]

I can also help out with the development.

[SouthEndMusic]

I'm working on a proof of concept, what's the best way to share that? Maybe Google colab?

[SouthEndMusic]

I started a repo: https://github.com/SouthEndMusic/NDimInterpolations.jl. I still have quite some ideas to work out. It's a mixture of DataInterpolations.jl and SplineGrids.jl (the latter can eventually be incorporated into this but linear interpolation is a nicer example to start with).

[SouthEndMusic]

The basic functionalities are inplace:

• Scalar and vector output
• In place and out of place evaluation
• single point evaluation
• Unstructured point set and point grid evaluation with KA, CUDAbackend compatible
• Partial derivatives

For those interested in the current API: you can render the docs locally, there is a usage section

[ChrisRackauckas]

NDInterpolations.jl might be a better name? If you're willing to move it into the org, we'd be happy to accept it. We can add it to the GSoC projects list as well, though it might be a little late to find a student. But I'd be happy to figure out some bounties to put on there as well, since it's a repo a lot of folks have been looking for.

[SouthEndMusic]

Sounds good, although I don't have time to mentor a student if applicable. What would moving the repo to the SciML org mean for the rights I have?

[ChrisRackauckas]

You can keep admin. And I just created @SciML/numerical-utilities which has some other similar libraries, we can put it in there and give maintain to the group.