Computational Health Center, Helmholtz Zentrum München Deutsches Forschungszentrum für Gesundheit und Umwelt (GmbH), Neuherberg, Germany.
School of Life Sciences, Technische Universität München, Freising, Germany.
PLoS One. 2024 Oct 23;19(10):e0312148. doi: 10.1371/journal.pone.0312148. eCollection 2024.
Estimating parameters of dynamic models from experimental data is a challenging, and often computationally-demanding task. It requires a large number of model simulations and objective function gradient computations, if gradient-based optimization is used. In many cases, steady-state computation is a part of model simulation, either due to steady-state data or an assumption that the system is at steady state at the initial time point. Various methods are available for steady-state and gradient computation. Yet, the most efficient pair of methods (one for steady states, one for gradients) for a particular model is often not clear. In order to facilitate the selection of methods, we explore six method pairs for computing the steady state and sensitivities at steady state using six real-world problems. The method pairs involve numerical integration or Newton's method to compute the steady-state, and-for both forward and adjoint sensitivity analysis-numerical integration or a tailored method to compute the sensitivities at steady-state. Our evaluation shows that all method pairs provide accurate steady-state and gradient values, and that the two method pairs that combine numerical integration for the steady-state with a tailored method for the sensitivities at steady-state were the most robust, and amongst the most computationally-efficient. We also observed that while Newton's method for steady-state computation yields a substantial speedup compared to numerical integration, it may lead to a large number of simulation failures. Overall, our study provides a concise overview across current methods for computing sensitivities at steady state. While our study shows that there is no universally-best method pair, it also provides guidance to modelers in choosing the right methods for a problem at hand.
从实验数据中估计动态模型的参数是一项具有挑战性的任务，通常需要大量的模型模拟和目标函数梯度计算，如果使用基于梯度的优化方法。在许多情况下，稳态计算是模型模拟的一部分，这要么是由于稳态数据，要么是因为假设系统在初始时间点处于稳态。有各种方法可用于稳态和梯度计算。然而，对于特定模型，最有效的一对方法（一个用于稳态，一个用于梯度）通常并不清楚。为了方便方法的选择，我们使用六个真实世界的问题来探索用于计算稳态和在稳态下的敏感性的六种方法对。这些方法对涉及数值积分或牛顿法来计算稳态，以及用于正向和伴随敏感性分析的数值积分或专门方法来计算在稳态下的敏感性。我们的评估表明，所有方法对都提供了准确的稳态和梯度值，并且将数值积分用于稳态与专门方法用于在稳态下的敏感性相结合的两种方法对是最稳健的，并且在计算效率方面也是最高的。我们还观察到，虽然牛顿法用于稳态计算与数值积分相比可以大大提高速度，但它可能导致大量的模拟失败。总的来说，我们的研究提供了对当前在稳态下计算敏感性的方法的简明概述。虽然我们的研究表明没有普遍最佳的方法对，但它也为建模者在选择适合手头问题的正确方法提供了指导。
