论文标题
基于参数近似优化的自动微分方程求解器
Automated differential equation solver based on the parametric approximation optimization
论文作者
论文摘要
微分方程解决方案的数值方法允许如果将方法应用于正确的问题，则获得离散的字段，该离散场会收敛到解决方案。然而，数值方法具有方程式的限制类别，在这些方程式上证明了具有给定参数集或范围的收敛性。只有几种“廉价和肮脏”的数值方法会在宽类方程式上收敛，而没有参数调整，而近似订单的价格较低。本文提出了一种使用优化算法来使用参数化近似来获得解决方案的方法。结果可能不如专家那样精确。但是，它允许以自动化方式求解宽类方程，而无需算法的参数更改。
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of the equations, on which the convergence with a given parameter set or range is proved. Only a few "cheap and dirty" numerical methods converge on a wide class of equations without parameter tuning with the lower approximation order price. The article presents a method that uses an optimization algorithm to obtain a solution using the parameterized approximation. The result may not be as precise as an expert one. However, it allows solving the wide class of equations in an automated manner without the algorithm's parameters change.
