(613d) Intrinsic Variables and the Consistent Reduction of Molecular Simulation Models
Chemical and molecular systems are inherently high-dimensional: reactors can contain tens or hundreds of chemical species participating in a reaction network, while macromolecules can contain hundreds or thousands of atoms. The dynamics of such systems can often be well described in fewer dimensions, and obtaining accurate reduced models can significantly enhance computer-assisted analysis. We propose to validate reduced dynamic models using nonlinear independent component analysis (NLICA) to compare full, high-dimensional simulation data and reduced, lower-dimensional simulations. NLICA [1,2] is a nonlinear dimensionality reduction technique that embeds a high-dimensional data set in a low-dimensional, intrinsic space; data sets resulting from different observations of the same underlying (stochastic) process will thus be mapped to a space spanned by the same intrinsic variables. By comparing the intrinsic variable embeddings of data sets produced from the full as well as the reduced models, we can quantitatively test their mutual consistency and validate the reduction process. We apply these techniques to different levels of macromolecular simulation. We also discuss how the approach can help suggest the number, and possibly the nature, of good coordinates for reduced complex system models.
 Amit Singer and Ronald R. Coifman, "Non-linear independent component analysis with diffusion maps," Applied and Computational Harmonic Analysis, vol. 25, no. 2, 2008.
 Amit Singer, Radek Erban, Ioannis G. Kevrekidis and Ronald R. Coifman, "Detecting intrinsic slow variables in stochastic dynamical systems by anisotropic diffusion maps," PNAS, vol. 106, no. 38, 2009.