On the Parameter Combinations That Matter and on Those That do Not

Abstract

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 effective parameters 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 redundant 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.

arXiv comment47 pages, 23 figures, 4 tables, submitted to PNAS Nexus, revised and expanded in response to reviewers' comments

References in corpus (10)

• Conditional Generative Adversarial Nets
• Neural Tangent Kernel: Convergence and Generalization in Neural Networks
• Universally Sloppy Parameter Sensitivities in Systems Biology
• Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations
• Why are nonlinear fits so challenging?
• Reduced models in chemical kinetics via nonlinear data-mining
• Manifold learning for parameter reduction
• Coarse-graining the Dynamics of a Driven Interface in the Presence of Mobile Impurities: Effective Description via Diffusion Maps
• Spectral Discovery of Jointly Smooth Features for Multimodal Data
• The underlying connections between identifiability, active subspaces, and parameter space dimension reduction