GSOC 2025: Implement adaptive uniformgrid refinement

[tutou2356]

Adds the AdaptiveUniformGrid wrapper class to provide recursive subdivision of a uniform grid.

[Ali-Tehrani]

Hi @tutou2356, these are my initial changes for the adaptive grid. Let me know if you have any questions/problems.

[Ali-Tehrani]

Hi Emily,

Thanks for your work, bug fixes that you found, and the requested changes! I tried it out with the gradient error measure and was disappointed with the integration improvement. Due to the time limit, I have made the following changes:

• Added a quadrature error measure that improves the integration error.
• The subdivision scheme now works over any axes, and vectorize it to make it faster
• Added an option to only do refinement if the integrand is higher than some threshold. This speeds up the refinement process.
• I removed the hash-map way of storing previous evaluated points. Any refinement that occurs should store the new points, their functional evaluations and weights automatically. This should speed things up (but I used hstack which can slow things).

I tried this out with some of your test-cases, and it improved the error measure. I would ignore the gentle_wide test cases, because symmetry places an important role in these functions. Additionally, I tried it out on the electron density, and it significantly improved the results. Therefore, I would recommend for your presentation to include electron density results, tutorials and various plots that you can think of.

Hope this helps you with your final evaluation.

[tutou2356]

Hi, Ali,
Thank you so much for the detailed updates and the new code. This is incredibly helpful.I'll be going through it in detail.
Thanks again for your guidance and support.