Machine Learning Based Optimization Workflow for Tuning Numerical
  Settings of Differential Equation Solvers for Boundary Value Problems
Viny Saajan Victor Manuel Ettmüller Andre Schmeißer Heike Leitte Simone Gramsch
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.