用轻量方法实现CAD模型的曲率正则化，训练更快更省显存。
FlatCAD: Fast Curvature Regularization of Neural SDFs for CAD Models
- 仅计算混合形状算子项，避免完整海森矩阵求导。
- 在ABC数据集上性能媲美或超越基线，显存与时间减半。
- 无需修改框架，适合工程级几何重建任务。
神经符号距离场（SDF）是神经几何表示的通用基础，但强制实现类CAD的可展性通常需要高斯曲率惩罚，涉及完整的海森矩阵计算和二阶微分，代价高昂。本文提出一种非对角魏因加滕损失，仅正则化代表主曲率差异的混合形状算子项，从而使表面趋于平坦。我们设计了两种变体：一种使用六次SDF评估加一次梯度的有限差分法，另一种采用单次海森向量积的自动微分法。两者均收敛至精确的混合项，且无需组装完整海森矩阵，同时保持预期几何特性。在ABC基准测试中，该方法性能匹配或超过基于海森矩阵的基线，同时将GPU内存占用和训练时间减少约一半。该方法即插即用、框架无关，支持可扩展的曲率感知SDF学习，适用于工程级形状重建。代码已开源：https://flatcad.github.io/。
原文摘要 · Abstract (English)
Neural signed-distance fields (SDFs) are a versatile backbone for neural geometry representation, but enforcing CAD-style developability usually requires Gaussian-curvature penalties with full Hessian evaluation and second-order differentiation, which are costly in memory and time. We introduce an off-diagonal Weingarten loss that regularizes only the mixed shape operator term that represents the gap between principal curvatures and flattens the surface. We present two variants: a finite-difference version using six SDF evaluations plus one gradient, and an auto-diff version using a single Hessian-vector product. Both converge to the exact mixed term and preserve the intended geometric properties without assembling the full Hessian. On the ABC benchmarks the losses match or exceed Hessian-based baselines while cutting GPU memory and training time by roughly a factor of two. The method is drop-in and framework-agnostic, enabling scalable curvature-aware SDF learning for engineering-grade shape reconstruction. Our code is available at https://flatcad.github.io/.
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