标题： 基于网格计算的GPU局部感知自动微分 显示英文标题

标题： Locality-Aware Automatic Differentiation on the GPU for Mesh-Based Computations

摘要： 我们提出了一种高性能系统，用于对定义在三角形网格上的函数进行自动微分（AD），该系统利用基于网格的能量函数的固有稀疏性和局部性，以在GPU上实现快速梯度和Hessian计算。 我们的系统围绕每个元素的前向模式微分设计，使所有局部计算保持在GPU寄存器或共享内存中。 与构建和遍历全局计算图的反向模式方法不同，我们的方法实时进行微分，最大限度地减少内存传输并避免全局同步。 我们的编程模型允许用户定义局部能量项，而系统处理并行评估、导数计算和稀疏Hessian组装。 我们在一系列应用上对系统进行了基准测试——布料模拟、表面参数化、网格平滑和球面流形优化。 对于二阶导数，我们的系统在优化的PyTorch实现上实现了几何平均加速6.2倍，对于Hessian-向量乘积实现了2.76倍加速。 对于一阶导数，我们的系统分别比Warp、JAX和Dr.JIT快6.38倍、2.89倍和1.98倍，同时与手写导数保持相当。 显示英文摘要

摘要： We present a high-performance system for automatic differentiation (AD) of functions defined on triangle meshes that exploits the inherent sparsity and locality of mesh-based energy functions to achieve fast gradient and Hessian computation on the GPU. Our system is designed around per-element forward-mode differentiation, enabling all local computations to remain in GPU registers or shared memory. Unlike reverse-mode approaches that construct and traverse global computation graphs, our method performs differentiation on the fly, minimizing memory traffic and avoiding global synchronization. Our programming model allows users to define local energy terms while the system handles parallel evaluation, derivative computation, and sparse Hessian assembly. We benchmark our system on a range of applications--cloth simulation, surface parameterization, mesh smoothing, and spherical manifold optimization. We achieve a geometric mean speedup of 6.2x over optimized PyTorch implementations for second-order derivatives, and 2.76x speedup for Hessian-vector products. For first-order derivatives, our system is 6.38x, 2.89x, and 1.98x faster than Warp, JAX, and Dr.JIT, respectively, while remaining on par with hand-written derivatives.