The predictive power of machine learning models often exceeds that of mechanistic modeling approaches. However, the interpretability of purely data-driven models, without any mechanistic basis is often complicated, and predictive power by itself can be a poor metric by which we might want to judge different methods. In this work, we focus on the relatively new modeling techniques of neural ordinary differential equations. We discuss how they relate to machine learning and mechanistic models, with the potential to narrow the gulf between these two frameworks: they constitute a class of hybrid model that integrates ideas from data-driven and dynamical systems approaches. Training neural ODEs as representations of dynamical systems data has its own specific demands, and we here propose a collocation scheme as a fast and efficient training strategy. This alleviates the need for costly ODE solvers. We illustrate the advantages that collocation approaches offer, as well as their robustness to qualitative features of a dynamical system, and the quantity and quality of observational data. We focus on systems that exemplify some of the hallmarks of complex dynamical systems encountered in systems biology, and we map out how these methods can be used in the analysis of mathematical models of cellular and physiological processes.

中文翻译：

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基于搭配的神经常微分方程训练

机器学习模型的预测能力通常超过机械建模方法。然而，没有任何机械基础的纯数据驱动模型的可解释性通常很复杂，而且预测能力本身可能是我们可能想要判断不同方法的一个糟糕的衡量标准。在这项工作中，我们专注于神经常微分方程的相对较新的建模技术。我们讨论了它们与机器学习和机械模型的关系，并有可能缩小这两个框架之间的鸿沟：它们构成了一类混合模型，整合了数据驱动和动态系统方法的想法。将神经 ODE 训练为动态系统数据的表示有其自身的特定需求，我们在此提出了一种搭配方案作为一种快速有效的训练策略。这减轻了对昂贵的 ODE 求解器的需求。我们说明了搭配方法提供的优势，以及它们对动态系统的定性特征以及观测数据的数量和质量的稳健性。我们专注于体现系统生物学中遇到的复杂动力系统的一些特征的系统，并绘制出如何将这些方法用于分析细胞和生理过程的数学模型。