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Interpolatory Surrogate Models for Light-Induced Transition Dynamics

MOKRAUER, DAVID SAMUEL. Interpolatory Surrogate Models for Light-Induced Transition Dynamics. (Under the direction of Dr. C. T. Kelley.) The potential energy of a molecule is a function of its geometry. Molecules observed naturally will be in conformations that minimize this potential energy and some molecules have multiple minima. In this dissertation, we develop algorithms that simulate transition paths between local energy minima through higher energy states. Computing the potential energy is an expensive optimization process that may fail due to poor initial iterates. An N atom molecule has 3N-6 degrees of freedom so the problem must be simplified to a few choice coordinates. Prior simulations rarely used more than a single degree of freedom. While this may be successful for a small molecule, simulations for larger molecules are not feasible with such simplification. We addressed some of the difficulties in computing the potential energy for specified geometries by developing continuation schemes. These continuation schemes incorporate pre-processing of some non-design variables for improved results. Our continuation methods run in parallel and exhibit good scalability. Simulation of the transitions is done by following the gradient flow. Even though our continuation methods make it possible to compute the potential energy at nearly any point in the design space, increasing the degrees of freedom in the simulation is still a burden because the energy computations are so expensive. We decreased the number of function evaluations by incrementally constructing cubic spline surrogates of the energy functional in small patches surrounding the gradient flow path. The tensor product grids required for the spline surrogate exhibit exponential complexity in the number of degrees of freedom. We are able to obtain polynomial complexity by replacing splines with Smolyak sparse interpolation. Finally we incorporate multiple error approximation and control schemes to maintain accuracy and decrease the simulation time. © Copyright 2012 by David Samuel Mokrauer