← 研踪 PaperTrailCVF · CVPR 2026:cvf:da369ccd88e00ff50a00559cbb0e8636 · 记录 #1
Learning to Solve PDEs on Neural Shape Representations
来源日期（仅到年份） 2026
来源记录日期 2026
雷达观测 2026-11-05 01:07
摘要
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, mesh-free formulation that learns a local update operator conditioned on neural (local) shape attributes, enabling surface PDEs to be solved directly where the (neural) data lives. The operator integrates naturally with prevalent neural surface representations, is trained once on a single representative shape, and generalizes across shape and topology variations, enabling accurate, fast inference without explicit meshing or per-instance optimization while preserving differentiability. Across analytic benchmarks (heat diffusion and Poisson equations on the sphere) and on diverse shapes and neural surface representations, our method achieves accuracy comparable to classical solvers while enabling a unified, end-to-end pipeline across neural and traditional surface representations. Our source code and project page: https://welschinger.github.io/Learning-to-Solve-PDEs-on-Neural-Shape-Representations/.
论文发现出处
这些页面提供论文线索，不代表同行评审或质量认证。
观测到的版本
平台记录号代表本站观测到的元数据变化，不是作者修订号。来源日期仅到月份或年份时，按该月或该年首日存档。
记录 #1 · 2026 · 最新观测版本
Learning to Solve PDEs on Neural Shape Representations
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, mesh-free formulation that learns a local update operator conditioned on neural (local) shape attributes, enabling surface PDEs to be solved directly where the (neural) data lives. The operator integrates naturally with prevalent neural surface representations, is trained once on a single representative shape, and generalizes across shape and topology variations, enabling accurate, fast inference without explicit meshing or per-instance optimization while preserving differentiability. Across analytic benchmarks (heat diffusion and Poisson equations on the sphere) and on diverse shapes and neural surface representations, our method achieves accuracy comparable to classical solvers while enabling a unified, end-to-end pipeline across neural and traditional surface representations. Our source code and project page: https://welschinger.github.io/Learning-to-Solve-PDEs-on-Neural-Shape-Representations/.
查看此版本解读 →查看此版本原文 ↗