直接有限时间收缩（步日志）剖面驱动的并行方案优化：多核架构上非线性问题的全部解高效计算
Direct Finite-Time Contraction (Step-Log) Profiling--Driven Optimization of Parallel Schemes for Nonlinear Problems on Multicore Architectures
AI总结：
本文提出一种基于直接有限时间收缩剖面的无训练调节框架，用于优化多核架构上非线性问题的并行方案，提升收敛率、稳定性和鲁棒性。
摘要：
非线性问题所有不同解的高效计算在许多科学和工程应用中至关重要。尽管高阶并行迭代方案提供快速收敛，但其实际性能往往受到内部参数敏感性和缺乏可重复调节过程的限制。基于解析条件和动态系统诊断的 classical 参数选择工具可能是问题依赖性的且计算开销大，这促使了轻量数据驱动的替代方案。在本研究中，我们提出了一种参数化的单步双参数并行Weierstrass型方案，具有三阶收敛性，以及基于直接有限时间收缩（步日志）剖面的无训练调节框架。该方法通过步范数和步日志比率直接从求解器轨迹中提取Lyapunov-like有限时间收缩信息，对微启动集合进行剖面聚合，并使用两个紧凑的评分：稳定性最小值S_min和稳定性矩S_mom对参数候选者进行排名。数值结果表明，在多样化的非线性测试问题中，收敛率、稳定性和鲁棒性都表现出一致的改进，确立了所提出的基于剖面的策略作为经典参数调节方法的高效且可重复的替代方案。
英文摘要：
Efficient computation of all distinct solutions of nonlinear problems is essential in many scientific and engineering applications. Although high-order parallel iterative schemes offer fast convergence, their practical performance is often limited by sensitivity to internal parameters and the lack of reproducible tuning procedures. Classical parameter selection tools based on analytical conditions and dynamical-system diagnostics can be problem-dependent and computationally demanding, which motivates lightweight data-driven alternatives. In this study, we propose a parameterized single-step bi-parametric parallel Weierstrass-type scheme with third-order convergence together with a training-free tuning framework based on Direct finite-time contraction (step-log) profiling. The approach extracts Lyapunov-like finite-time contraction information directly from solver trajectories via step norms and step-log ratios, aggregates the resulting profiles over micro-launch ensembles, and ranks parameter candidates using two compact scores: the stability minimum S_min and the stability moment S_mom. Numerical results demonstrate consistent improvements in convergence rate, stability, and robustness across diverse nonlinear test problems, establishing the proposed profiling-based strategy as an efficient and reproducible alternative to classical parameter tuning methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
