Several numerical differential equation solvers have been employed effectively over the years as an alternative to analytical solvers to quickly and conveniently solve differential equations. One category of these is boundary value solvers, which are used to solve real-world problems formulated as differential equations with boundary conditions. These solvers require certain numerical settings to solve the differential equations that affect their solvability and performance. A systematic fine-tuning of these settings is required to obtain the desired solution and performance. Currently, these settings are either selected by trial and error or require domain expertise. In this paper, we propose a machine learning-based optimization workflow for fine-tuning the numerical settings to reduce the time and domain expertise required in the process. In the evaluation section, we discuss the scalability, stability, and reliability of the proposed workflow. We demonstrate our workflow on a numerical boundary value problem solver.

翻译：多年来，多种数值微分方程求解器被有效用于替代解析求解器，以快速便捷地求解微分方程。其中一类是边界值求解器，用于求解以带边界条件的微分方程形式表述的实际问题。这些求解器需要特定的数值设置来求解微分方程，这些设置会影响求解器的可解性与性能。为获得理想的解及性能，需对这些设置进行系统性微调。目前，这些设置要么通过试错法选择，要么需要领域专业知识。本文提出一种基于机器学习的优化工作流，用于微调数值设置，以降低该过程所需的时间和领域专业知识。在评估部分，我们讨论了所提工作流的可扩展性、稳定性和可靠性。我们在一个数值边界值问题求解器上展示了该工作流的应用。