Many processes in science and engineering can be described by dynamical systems based on nonlinear ordinary differential equations (ODEs). Often ODE parameters are unknown and not directly measurable. Since nonlinear ODEs typically have no closed form solution, standard iterative inference procedures require a computationally expensive numerical integration of the ODEs every time the parameters are adapted, which in practice restricts statistical inference to rather small systems. To overcome this computational bottleneck, approximate methods based on gradient matching have recently gained much attention. The idea is to circumvent the numerical integration step by using a surrogate cost function that quantifies the discrepancy between the derivatives obtained from a smooth interpolant to the data and the derivatives predicted by the ODEs. The present article describes the software implementation of a recent method that is based on the framework of reproducing kernel Hilbert spaces. We provide an overview of the methods available, illustrate them on a series of widely used benchmark problems, and discuss the accuracy–efficiency trade-off of various regularization methods.

可以通过基于非线性常微分方程（ODE）的动力学系统来描述科学和工程学中的许多过程。ODE参数通常是未知的，无法直接测量。由于非线性ODE通常没有封闭形式的解决方案，因此，标准的迭代推理过程每次在对参数进行调整时都需要ODE的计算量大的数值积分，这实际上将统计推断限制在相当小的系统上。为了克服这个计算瓶颈，基于梯度匹配的近似方法最近引起了很多关注。这个想法是通过使用替代成本函数来规避数值积分步骤，该函数对从平滑插值数据获得的导数与ODE预测的导数之间的差异进行量化。本文介绍了一种基于复制内核Hilbert空间的框架的最新方法的软件实现。我们提供了可用方法的概述，在一系列广泛使用的基准问题上对其进行了说明，并讨论了各种正则化方法的准确性与效率之间的取舍。