Modeling and Control of State-Affine Probabilistic Systems for Atomic- Scale Dynamics.

摘要

Under this research grant, the framework and tools were developed for model reduction of atomic-scale many body systems. The state-affine mathematical structure of the original and reduced order models enabled the implementation of control through dynamic programming and estimation through an extended Kalman filter. The state of the high-dimensional stochastic system is first quantified using a high-dimensional pair correlation function. This state is then reduced using linear and nonlinear principal component analysis and is discretized using self-organizing maps. To create the dynamic model, a cell map is constructed using short simulations to quantify input-dependent transitions between the discrete states. The error associated with the model reduction was quantified and analyzed, and a method for predicting this error was proposed. Specific applications in materials processing were considered, which motivated and guided the development of the model reduction framework and tools. An existing model of gallium arsenide deposition was used to demonstrate the model reduction framework. A second modeling study in the molecular architecture of hyperbranched polymers was performed, and enabled a comparison of common themes and system specific features between the two different applications.