Nonlinear Data Mining and Parameter Reduction in Complex Reaction Networks

While there has been extensive work in reducing the number of variables in large, complex dynamic models, leading to models of smaller dimension, work on concomitant reduction in the number of parameters is a relatively recent endeavor; “sloppiness” and active subspaces are two promising current directions. In this paper we will explore the link between (nonlinear) data mining (via Diffusion Maps) and parameter reduction by analyzing “good” parameter sets, and determining their dimension and possible parameterizations. Combining equation-free principles with machine learning algorithms, we propose a data-based approach to resolve “sloppy” parameter directions in both singularly- and regularly-perturbed complex kinetic models, and employ it to speed up and hopefully improve parameter-fitting routines.