Data-Driven Coarse-Graining using Space-Time Diffusion Maps

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Dynamical systems with many degrees of freedom arise in a wide range of applications, including large scale molecular dynamics, climate and weather studies, and electrical power networks. The challenge in simulation is normally to extract statistical information, for example the average propensity of a given state of the system or the average time that elapses between certain events. Simulation data is easy to generate but often poorly utilized. The goal of this project is the development of a data-driven method for the automatic detection of a simplified description of the system based on a set of collective variables which can be used within efficient statistical extraction procedures. These slowest degrees of freedom are typically the most important ones. The dynamics are characterised as fluctuations in the vicinity of given state punctuated by relatively rare events describing transitions between the states. Efficiently identifying collective variables is the crucial first step in the design of coarse-grained models which can allow many order of magnitude increases in the accessible simulation timescale. By automatically finding collective variables, we can greatly simplify rapid study and comparison of many systems. The research builds on the technique of diffusion maps, whereby the eigenfunctions of a diffusion operator are used to characterise the metastable (slowly changing) states of the system. The potential impact of automatic coarse-graining will be felt most profoundly in fields such as rational drug design, where it is necessary to select specific drug molecules for their properties in interaction with some target, e.g. a protein. Bio-molecular simulation depends on the use of very specialised and intensely developed simulation codes which are the products of many years of development and government investment. In order to accelerate the implementation and testing of novel algorithms in this important area, this project includes a detailed plan for software development within the EPSRC-funded MIST (Molecular Integrator Software Tools) platform. Testing of the software methodology will be conducted via collaborations with chemists and pharmaceutical chemists, including researchers at Rice University (Houston, Texas) and Memorial Sloan Kettering Cancer Research Center (New York).