Cleanup function spec, plus adding a few functionals

[loliverhennigh]

PhysicsNeMo Pull Request

Description

This PR is a cleanup pass for physicsnemo.nn.functional plus interpolation/test/benchmark updates. This PR will be followed by one more concentrated on CI integration with Github actions.

What’s included:

• Reorganized functionals into clearer category folders (fourier_spectral, geometry, neighbors, interpolation, regularization_parameterization). This mimics the Docs while not changing API or import paths. Imports still come from nn.functional.xyz, this is cleans stuff up internally.
• Migrated interpolation to the newer grid_to_point_interpolation structure with proper warp support and backward pass. Also added a point_to_grid_interpolation for fun and completness.
• Added two other functionals from ongoing work, mesh_to_voxel_fraction and mesh_poisson_disk_sample. If its too much to review these I can remove them.
• Updated unit tests for functionals so they all follow the same structure. This required some small but important changes with base FunctionSpec implementation.
• Refreshed benchmark scripts/registry and docs paths so plots/docs line up with the new organization.

Overall goal: make functionals easier to navigate, easier to test, and easier to benchmark.

[loliverhennigh]

We now run benchmarks on forward and backward (if backward exists). I generate two bar plots now for these instead of just the forward pass before.

[loliverhennigh]

Again, these files are kinda throw away until I have the ASV setup with the CI/CD system.

[greptile-apps]

Greptile Summary

This PR successfully reorganizes the functional architecture into clearer category folders while maintaining backward compatibility and improving the interpolation implementation.

Key Changes

• Functional Reorganization: Moved functionals into category folders (fourier_spectral, geometry, neighbors, interpolation, regularization_parameterization). Public API imports remain unchanged, maintaining backward compatibility.

• Interpolation Improvements: Migrated to new grid_to_point_interpolation with proper Warp support, backward pass implementation, and comprehensive test coverage. The old interpolation function is deprecated with a warning.

• FunctionSpec Enhancements: Added make_inputs_forward/make_inputs_backward and compare_forward/compare_backward methods while maintaining backward compatibility with old make_inputs/compare API through fallback hooks.

• Benchmark Infrastructure: Enhanced ASV benchmarks with forward/backward phase support, environment-based filtering, and improved label extraction without full tensor materialization.

• Documentation: Updated CODING_STANDARDS/FUNCTIONAL_APIS.md to reflect new patterns and added FNC-007 rule for benchmark registry.

Code Quality

The refactoring is well-executed with:

• Comprehensive test coverage including backend parity, error handling, and backward pass validation
• Clean separation of concerns with backend implementations in dedicated modules
• Proper adherence to the documented coding standards (FNC-000 through FNC-007)
• Backward compatibility maintained throughout

Notes

Several functionals (KNN, RadiusSearch, SignedDistanceField) have compare methods marked with TODO comments to implement output comparison in a follow-up PR. This is intentional and doesn't block the current refactoring.

Important Files Changed

Filename	Overview
physicsnemo/nn/functional/init.py	Updated imports to reflect reorganized functional structure into category folders (fourier_spectral, geometry, neighbors, regularization_parameterization). Added grid_to_point_interpolation export. Public API remains unchanged.
physicsnemo/core/function_spec.py	Added backward-compatible hooks for make_inputs_forward/backward and compare_forward/backward while maintaining old make_inputs/compare methods. Added label extraction helpers. Well-structured backward compatibility.
physicsnemo/nn/functional/interpolation/grid_to_point_interpolation/grid_to_point_interpolation.py	New grid_to_point_interpolation implementation with warp and torch backends. Includes backward pass support, proper tolerance configuration, and deprecation alias for old interpolation function. Follows FunctionSpec patterns correctly.
test/nn/functional/test_grid_to_point_interpolation_functional.py	Comprehensive test coverage for grid_to_point_interpolation including backend parity tests, error handling, deprecation warnings, backward pass validation, and non-contiguous input handling.
benchmarks/physicsnemo/nn/functional/registry.py	Updated registry to include all reorganized FunctionSpec classes (DropPath, KNN, GridToPointInterpolation, RadiusSearch, SignedDistanceField, RFFT, RFFT2, IRFFT, IRFFT2) for ASV benchmarking.
benchmarks/physicsnemo/nn/functional/benchmark_functionals.py	Enhanced benchmark infrastructure with forward/backward phase support, environment-based phase filtering, gradient clearing for reusable inputs, and label extraction without full materialization.
physicsnemo/nn/functional/neighbors/knn/knn.py	Moved to neighbors folder with custom dispatch for device-based auto-selection. Has TODO for compare method implementation. Properly implements make_inputs_forward/backward.
CODING_STANDARDS/FUNCTIONAL_APIS.md	Updated documentation to reflect make_inputs_forward/backward and compare_forward/backward patterns. Added FNC-007 rule for benchmark registry. Documentation aligns with implementation changes.

_{Last reviewed commit: a1183b8}

[greptile-apps]

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[loliverhennigh]

Code in the benchmarks is still a bit junky.