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Abstract

We propose an approach for summarizing the output of long simulations of complex systems, affording a rapid overview and interpretation. First, multidimensional scaling techniques are used in conjunction with dimension reduction methods to obtain a low-dimensional representation of the configuration space explored by the system. A nonparametric estimate of the density of states in this subspace is then obtained using kernel methods. The free energysurface is calculated from that density, and the configurations produced in the simulation are then clustered according to the topography of that surface, such that all configurations belonging to one local free energy minimum form one class. This topographical cluster analysis is performed using basin spanning trees which we introduce as subgraphs of Delaunay triangulations. Free energysurfaces obtained in dimensions lower than four can be visualized directly using iso-contours and -surfaces. Basin spanning trees also afford a glimpse of higher-dimensional topographies. The procedure is illustrated using molecular dynamics simulations on the reversible folding of peptide analoga. Finally, we emphasize the intimate relation of density estimation techniques to modern enhanced sampling algorithms.