This paper considers the hyperparameter optimization problem of mathematical techniques that arise in the numerical solution of differential and integral equations. The well-known approaches grid and random search, in a parallel algorithm manner, are developed to find the optimal set of hyperparameters. Employing rational Jacobi functions, we ran these algorithms on two nonlinear benchmark differential equations on the semi-infinite domain. The configurations contain different rational mappings along with their length scale parameter and the Jacobi functions parameters. These trials are configured on the collocation Least-Squares Support Vector Regression (CLS-SVR), a novel numerical simulation approach based on spectral methods. In addition, we have addressed the sensitivity of these hyperparameters on the numerical stability and convergence of the CLS-SVR model. The experiments show that this technique can effectively improve state-of-the-art results.

翻译：本文研究了微分与积分方程数值求解中数学技术的超参数优化问题。以并行算法方式发展了广为人知的网格搜索与随机搜索方法，用于寻找最优超参数集。采用有理雅可比函数，在半无限域上的两个非线性基准微分方程中运行这些算法。配置包含不同有理映射及其长度尺度参数和雅可比函数参数。这些试验基于配置点最小二乘支持向量回归（CLS-SVR）——一种基于谱方法的新型数值模拟方法。此外，我们探讨了这些超参数对CLS-SVR模型数值稳定性和收敛性的敏感性。实验表明，该技术能有效改进当前最优结果。