Mesh: Add differentiable exact RBF mesh morphing

[mehdiataei]

PhysicsNeMo Pull Request

Description

This PR adds dimensionally generic thin-plate-spline radial basis function (RBF) morphing for points and meshes.

The new APIs include:

• rbf_morph_points for batched or unbatched tensor inputs.
• Mesh.rbf_morph for individual meshes.
• DomainMesh.rbf_morph for applying one fitted field across all domain components.

PyTorch performs the differentiable coefficient solve. Field evaluation supports both PyTorch and a fused NVIDIA Warp backend, with automatic device-based dispatch. The implementation supports an optional affine polynomial tail, smoothing, and per-point weights. With zero smoothing, the fitted field interpolates control displacements before optional point weights are applied.

The PyTorch implementation supports first- and second-order gradients. The Warp evaluator supports first-order gradients through query points, control locations, control displacements, and floating-point weights. Input validation reports invalid layouts and singular control systems with actionable errors.

Documentation includes reproducible 2D and 3D examples and visualizations.

Validation completed:

• 475 tests passed with 22 expected skips.
• PyTorch gradcheck and gradgradcheck passed.
• PyTorch/Warp forward and backward parity tests passed.
• Dynamic and compiled execution tests passed.
• All pre-commit hooks passed.
• The documentation build completed successfully.

Checklist

• I am familiar with the Contributing Guidelines.
• New or existing tests cover these changes.
• The documentation is up to date with these changes.
• The CHANGELOG.md is up to date with these changes.
• An issue is linked to this pull request.
• If I am implementing a new model or modifying any existing model, I have followed the Models Implementation Coding Standards. (Not applicable; no model code was changed.)

Dependencies

No new dependencies.

Review Process

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[greptile-apps]

Greptile Summary

This PR adds exact RBF morphing for tensors and meshes. The main changes are:

• New rbf_morph_points functional with Torch fitting and Torch/Warp evaluation.
• New Mesh.rbf_morph and DomainMesh.rbf_morph APIs.
• Shared DomainMesh deformation helper for combined component evaluation.
• Warp kernels and custom-op bindings for RBF field evaluation.
• Documentation, examples, benchmarks, and broad RBF test coverage.

Important Files Changed

Filename	Overview
physicsnemo/nn/functional/geometry/deform/rbf.py	Adds the public RBF morph functional, validation, backend dispatch, and benchmark cases.
physicsnemo/nn/functional/geometry/deform/_rbf_torch_impl.py	Adds Torch-side TPS coefficient fitting and chunked field evaluation.
physicsnemo/nn/functional/geometry/deform/_warp_impl/rbf_op.py	Adds Warp custom-op integration and autograd registration for RBF field evaluation.
physicsnemo/nn/functional/geometry/deform/_warp_impl/rbf_kernels.py	Adds Warp kernels for TPS forward evaluation and first-order pullbacks.
physicsnemo/mesh/domain_mesh.py	Adds DomainMesh RBF morphing and factors shared component deformation logic.
physicsnemo/mesh/transformations/deform/rbf.py	Adds the Mesh-level RBF morph wrapper around the tensor functional.
physicsnemo/mesh/transformations/deform/_utils.py	Adds shared DomainMesh point-weight and component validation helpers.
test/nn/functional/geometry/test_rbf_morph.py	Adds tensor-level RBF tests for interpolation, validation, gradients, Warp parity, and compile paths.
test/mesh/transformations/test_mesh_rbf_morph.py	Adds Mesh and DomainMesh integration tests for RBF morphing.

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