Learning to Solve PDEs on Neural Shape Representations

arXiv:2512.21311v2 Announce Type: replace Abstract: Solving partial differential equations (PDEs) on shapes underpins many shape analysis and engineering tasks; yet, prevailing PDE solvers operate on polygonal/triangle meshes while modern 3D assets increasingly live as neural representations. This mismatch leaves no suitable method to solve surface PDEs directly within the neural domain, forcing explicit mesh extraction or per-instance residual training, preventing end-to-end workflows. We present a novel, meshfree formulation that learns a local update operator conditioned on neural (local) s

Source: arXiv cs.LG — read the full report at the original publisher.

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