Mesh: GPU-Accelerated Differentiable Deformation Energies

[mehdiataei]

PhysicsNeMo Pull Request

Description

Adds GPU-accelerated, differentiable deformation-energy functionals for fixed-topology engineering meshes.

The new tensor APIs include:

• simplex_strain_energy
• simplex_measure_energy
• total_measure_energy
• simplex_inversion_energy
• surface_bending_energy
• closed_surface_volume_energy

Torch implementations support higher-order differentiation and dimensionally generic simplex geometry. NVIDIA Warp implementations provide first-order GPU acceleration for supported coordinate dimensions. Mesh-aware wrappers validate and cache topology, construct triangle hinges, and expose the energies through physicsnemo.mesh.deformation.

The implementation handles batched coordinates, configurable reductions, invalid and degenerate geometry, empty topology, extreme coordinate scales, auxetic material parameters, and numerically challenging slender simplices. Torch and Warp behavior is covered by forward, gradient, compilation, dispatch, topology, and backend-parity tests.

Documentation includes 2D and 3D optimization examples with generated figures demonstrating area, inversion, volume, and bending regularization.

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 models are added or modified.)

Dependencies

No new dependencies.

Review Process

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