发表机构
University of Notre Dame; Cornell University（圣母大学; 康奈尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
Warp-Geo提出一种可微GPU框架，结合均匀网格与隐式微分，实现点云SDF重建、动态边界模拟及形状优化，支持频繁几何更新。
AI 中文摘要
现代逆问题和自适应模拟需要复杂几何的高效且可微的表示，这些几何可以频繁更新以用于基于梯度的优化。现有方法无法同时实现这两点。我们提出了Warp-Geo，一个可微的GPU加速框架，用于从复杂3D几何的点云重建符号距离场并评估表面法线。Warp-Geo将用于GPU并行的均匀网格与通过泊松求解的隐式微分相结合，在保持完全可微性的同时实现频繁的几何重计算。我们在前向SDF重建、具有移动边界的动态流固耦合以及通过自动微分和梯度验证的逆形状优化上展示了Warp-Geo。GPU可扩展性分析证实了频繁几何更新的实际可行性。该框架在Warp和JAX中实现，能够与可微物理求解器无缝集成，用于端到端的形状优化。
英文摘要
Modern inverse problems and adaptive simulations require efficient and differentiable representations of complex geometries that can be updated frequently for gradient-based optimization. Existing methods cannot simultaneously achieve both. We present Warp-Geo, a differentiable GPU-accelerated framework for reconstructing signed distance fields and evaluating surface normals from point clouds of complex 3D geometries. Warp-Geo combines uniform grids for GPU parallelism with implicit differentiation through the Poisson solve, enabling frequent geometry recomputation while maintaining full differentiability. We demonstrate Warp-Geo on forward SDF reconstruction, dynamic fluid--structure interaction with moving boundaries, and inverse shape optimization via automatic differentiation with gradient validation. GPU scalability analysis confirms practical feasibility for frequent geometry updates. The framework, implemented in Warp and JAX, enables seamless integration with differentiable physics solvers for end-to-end shape optimization.
Comments35 pages, 14 figures
