Dimension Reduction, Coarse-Graining and Data Assimilation in High-Dimensional Dynamical Systems

Dimension Reduction, Coarse-Graining and Data Assimilation in High-Dimensional Dynamical Systems

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Eric Vanden-Eijnden, Courant NYU
Fine Hall 214

Modern computing technologies, such as massively parallel simulation, special-purpose high-performance computers, and high-performance GPUs permit to simulate complex high-dimensional dynamical systems and generate time-series in amounts too large to be grasped by traditional “look and see” analyses. This calls for robust and automated methods to extract the essential structural and dynamical properties from these data in a manner that is little or not depending on human subjectivity. To this end, a decade of work has led to the development of analysis techniques which rely on the partitioning of the conformation space into discrete substates and reduce the dynamics to transitions between these states. A particular successful class of methods of this type are Markov state models (MSMs), in which the transitions between the states in the partition are assumed to be memoryless jumps. The accuracy of these models crucially depends on the choice of these states. In this talk, I will discuss systematic strategies that permit to identify these states and quantify the error of the resulting approximation. These methods will be illustrated on examples arising from molecular dynamics simulations of biomolecules.