Validating Reduced Models Using Nonlinear Independent Component Analysis

Carmeline Dsilva, Princeton University

Many interesting and important systems in chemistry and physics are inherently high-dimensional. For example, macromolecular simulations can involve the motions of hundreds or thousands of atoms, and chemical reaction networks can involve tens or hundreds of species. It is often assumed that the dynamics of the system can be usefully approximated by a lower-dimensional representation (i.e. coarse-graining large polymers into several “beads” or applying the quasi-steady-state approximation to a chemical reaction network), but there are few rigorous methods by which to test the validity of such assumptions. We propose a data-driven approach to implementing a useful comparison between a full, high-dimensional model and its lower-dimensional approximation. We collect data from simulations of both the high-dimensional and the lower-dimensional models. Using nonlinear independent component analysis, a nonlinear dimensionality reduction technique, we produce a low-dimensional, intrinsic embedding of the data from each model. We then compare the embeddings and test whether both models approximate the same effective, coarse-grained dynamical process. We apply this methodology to a chemical reaction network as well as a molecular dynamics simulation of a macromolecule.

Abstract Author(s): Carmeline Dsilva, Ioannis Kevrekidis