(555d) Data-Driven Methods for the Analysis of Multiscale Stochastic Systems

Authors: 
Dsilva, C., Princeton University
Kevrekidis, I. G., Princeton University
Talmon, R., Yale University
Coifman, R., Yale University

Complex dynamic engineering models often contain dynamical processes evolving over broad ranges of time and length scales. Separation of timescales can pose problems in modeling and simulation, as accurately resolving the fast modes on timescales which are relevant for the slow modes requires significant computational power. Reducing the model to only contain the slow modes is often based on a priori knowledge or analytic transformations of the variables, which may not be immediately obvious for complex systems. We propose data-driven techniques which automatically uncover the slow variables from simulation data. Using nonlinear independent component analysis [1, 2], a nonlinear dimensionality reduction technique, we show that we can recover the slow variables, even when the system dynamics are complex and nonlinear. We demonstrate our methods through examples from chemical reaction networks and molecular simulations.

[1] Singer, Amit, and Ronald R. Coifman. "Non-linear independent component analysis with diffusion maps." Applied and Computational Harmonic Analysis25.2 (2008): 226-239.

[2] Dsilva, Carmeline J., et al. "Nonlinear intrinsic variables and state reconstruction in multiscale simulations." The Journal of chemical physics 139.18 (2013): 184109.