AI 中文总结
ExaModels.jl是基于Julia的代数建模系统，利用非线性规划的重复结构并行计算，适配GPU并行性，在多个基准测试集上大幅提升了稀疏海森矩阵的计算速度。
AI 中文摘要
大规模非线性规划问题几乎都呈现出部分可分性与重复结构，但现有大多数代数建模系统并未利用这一特性。非线性优化求解器在每次迭代时都会查询目标函数、约束条件及其导数，因此这些计算的速度直接影响整体求解时间。本文介绍ExaModels.jl，这是一个基于Julia的代数建模系统，可利用上述结构并行计算目标函数、约束条件及其导数。其核心是单指令多数据抽象，将非线性规划表示为少量代数模式，每个模式在大量数据点上重复出现。由于这些模式在编译时即可见，系统会为每个模式编译专用的模型与导数计算内核。将该内核独立应用于各数据点，可自然适配GPU并行性，且在拥有足够多线程时，无论数据点数量多少，都能实现O(1)级别的计算时间。在Luksan-Vlcek库的最大实例上，GPU执行的稀疏海森矩阵计算速度比单线程CPU快76倍；在COPS基准测试集上快30倍，在PGLIB-OPF基准测试集上快7.3倍。
英文摘要
Large-scale nonlinear programs almost always exhibit partially separable and repetitive structure, yet most existing algebraic modeling systems do not take advantage of it. A nonlinear optimization solver queries the objective, the constraints, and their derivatives at every iteration, so the speed of these evaluations bears directly on the overall solution time. We present ExaModels.jl, a Julia-based algebraic modeling system that exploits this structure to evaluate the objective, the constraints, and their derivatives in parallel. At its core is a single-instruction, multiple-data abstraction that represents a nonlinear program as a small number of algebraic patterns, each repeated over many data points. Because the patterns are visible at compile time, a specialized model and derivative evaluation kernel is compiled for each pattern. Applying that kernel independently across the data points maps naturally onto GPU parallelism and, with sufficiently many threads, yields O(1) evaluation time regardless of the number of data points. On the largest instances of the Luksan-Vlcek library, GPU execution speeds up sparse Hessian evaluation by 76x over single-threaded CPU evaluation, and by 30x on COPS and 7.3x on PGLIB-OPF.
