Evangelou Nikolaos, Wichrowski Noah J, Kevrekidis George A, Dietrich Felix, Kooshkbaghi Mahdi, McFann Sarah, Kevrekidis Ioannis G
Department of Chemical and Biomolecular Engineering, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA.
Department of Applied Mathematics and Statistics, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA.
PNAS Nexus. 2022 Sep 14;1(4):pgac154. doi: 10.1093/pnasnexus/pgac154. eCollection 2022 Sep.
We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the output behavior of a chemical system: a set of for the model. Furthermore, we introduce and use a Conformal Autoencoder Neural Network technique, as well as a kernel-based Jointly Smooth Function technique, to disentangle the parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters, and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters (nonlinear combinations of the physical ones) has previously been established analytically.
我们提出了一种数据驱动的方法来表征模型参数的不可识别性，并通过动态和稳态动力学模型对其进行说明。通过使用扩散映射及其扩展，我们发现了表征化学系统输出行为所需的参数的最小组合：该模型的一组 。此外，我们引入并使用了共形自动编码器神经网络技术以及基于核的联合平滑函数技术，以区分不影响输出行为的参数组合和影响输出行为的参数组合。我们讨论了数据驱动的有效参数的可解释性，并展示了该方法在行为预测和参数估计方面的效用。在后一项任务中，描述与特定输出行为一致的参数空间中的水平集变得很重要。我们在多位点磷酸化模型上验证了我们的方法，在该模型中，先前已经通过分析建立了一组简化的有效参数（物理参数的非线性组合）。
