Diffusion maps for model reduction: exploiting data mining to accelerate simulation

Benjamin Sonday, Princeton University

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In many complex/multiscale systems, the long-term dynamics are reducible: they lie on a low-dimensional manifold parametrized by appropriate coarse variables (observables). Knowing these observables a priori, through experience or intuition, can be crucial in accelerating the computational extraction of information from detailed, “fine scale” simulators. Indeed, when such variables parametrizing the slow dynamics are known, the so-called equation-free approach provides a systematic way of designing computational “wrappers” that enable fine scale simulators to perform accelerated simulation as well as a wide range of additional tasks (coarse-grained stability and bifurcation computations, parametric continuation, coarse controller design, etc.).

When such coarse observables are not known, data mining tools can be used to extract them from simulation databases. Linking data-mining tools (and, in particular, the diffusion map approach of Coifman and coworkers) and the design of equation-free computational experiments provides an integrated framework for coarse-grained computations of complex/multiscale systems.

Abstract Author(s): B. Sonday, A. Singer, I. G. Kevrekidis