Mesh: fix padding for discrete data and cached centroids

[peterdsharpe]

PhysicsNeMo Pull Request

Description

Mesh.pad() previously failed on integer and boolean data with its default NaN fill. A previously cached cell centroid could also disagree with the geometry of a padded cell, making the result depend on whether the cache had already been populated.

This PR:

• Uses zero for default padding of fields that cannot represent NaN, preserving their dtype.
• Supports empty-mesh padding and rejects the impossible case of creating cells without any point.
• Keeps cached padded-cell centroids consistent with their repeated point.
• Adds regression coverage for discrete fields, empty meshes, cached centroids, and the low-level tiling helper.

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.

Dependencies

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[peterdsharpe]

/ok to test 7c46948

[greptile-apps]

Greptile Summary

This PR fixes two bugs in Mesh.pad(): integer and boolean data fields previously raised an error when padded with the default NaN fill value, and a previously cached cell centroid could disagree with the geometry of padded degenerate cells. It also extends padding to support empty meshes and guards against the impossible case of creating cells with no points.

• Dtype-safe padding: _pad_data now checks is_floating_point() / is_complex() and substitutes 0 for NaN on discrete tensors, preserving their dtype without breaking the public API.
• Centroid cache consistency: After the standard zero-fill apply() populates padded_cell_cache, centroids are overridden with self.points[-1:] (or zeros for an empty mesh), matching the actual point each degenerate cell references.
• Empty-mesh support: _pad_by_tiling_last short-circuits to new_zeros when the source tensor is empty, and pad() rejects the logically impossible target_n_cells > 0 + target_n_points == 0 combination.

Important Files Changed

Filename	Overview
physicsnemo/mesh/mesh.py	Fixes pad() to use 0 instead of NaN for integer/boolean fields, validates the empty-point + non-zero-cell case, and overrides the 0-padded cached centroids with the geometrically correct last-point value.
physicsnemo/mesh/utilities/_padding.py	Adds an early-return guard in _pad_by_tiling_last for empty tensors; returns zero-filled rows instead of attempting tensor[-1:] on a 0-row tensor.
test/mesh/mesh/test_padding.py	Adds regression tests for discrete field dtype preservation, empty mesh padding, cached centroid consistency, and the impossible case of creating cells on a zero-point mesh.
test/mesh/utilities/test_utilities.py	Adds a unit test for _pad_by_tiling_last with an empty input tensor, confirming zero-row output.

_{Reviews (1): Last reviewed commit: "fix(mesh): handle padding edge cases" | Re-trigger Greptile}

[melo-gonzo]

LGTM!