发表机构
Institut Teknologi Sepuluh Nopember; Khalifa University of Science & Technology（泗水理工学院; 哈利法科学技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出混合联合-选择性优化框架，通过联合一阶优化与降维LM精化结合，高效优化低维感兴趣参数，在多个大规模问题上加速收敛并提升精度。
AI 中文摘要
本文提出了一种用于大规模数值问题的混合联合-选择性优化（HJSO）框架，其中一小部分可训练量是主要关注对象。我们将完整参数向量划分为高维剩余块和低维感兴趣参数（POIs）块，在完整参数集上执行联合一阶优化，然后冻结剩余变量，同时对POIs应用降维Levenberg-Marquardt（LM）精化。该方法专为POIs维度低但对计算结果质量有强烈影响，而完整参数空间对于全空间二阶方法而言过大的场景而设计。该框架在三个代表性问题上进行了评估：矩阵特征值问题、用物理信息神经网络求解的逆Bratu问题，以及用DeepBSDE方法求解的100维非线性Black-Scholes问题。在每个测试中，HJSO达到指定POI误差阈值的时间均快于相应的联合一阶基线，并在所报告的求解器配置下提高了最终POI精度。因此，其贡献并非一种通用优化器，而是一种针对已知低维感兴趣参数和昂贵高维训练变量的实际降维策略。
英文摘要
This paper introduces a hybrid joint-selective optimization (HJSO) framework for large-scale numerical problems in which a small subset of trainable quantities is of primary interest. We partition the full parameter vector into a high-dimensional remaining block and a low-dimensional block of parameters of interest (POIs), perform joint first-order optimization over the full parameter set, and then freeze the remaining variables while applying a reduced-space Levenberg-Marquardt (LM) refinement to the POIs. The method is designed for settings in which the POIs are low-dimensional but strongly influence the quality of the computed solution, while the full parameter space remains too large for full-space second-order methods. The framework is evaluated on three representative problems: a matrix eigenvalue problem, an inverse Bratu problem solved with a physics-informed neural network, and a 100-dimensional nonlinear Black-Scholes problem solved with the DeepBSDE method. In each test, HJSO reaches prescribed POI-error thresholds faster than the corresponding joint first-order baseline and improves the final POI accuracy for the reported solver configurations. The contribution is therefore not a universal optimizer, but a practical reduced-space strategy for problems with known low-dimensional parameters of interest and expensive high-dimensional training variables.
