Numerical Solution of Optimal Control Problem under SPDE Constraints

Abstract : The overall goal of this AFOSR sponsored research program is to construct fast and efficient numerical algorithms for solving stochastic partial differential equations and apply them to solve optimal control problems under uncertainty which is described by stochastic partial differential equations. It is well understood that effective numerical methods for stochastic partial differential equations (SPDES) are essential for uncertainty quantification. In the last decade much progress has been made in the construction of numerical algorithms to efficiently solve SPDES with random coefficients and white noise perturbations. However, high dimensionality and low regularity are still the bottleneck in solving real world applicable SPDES with efficient numerical methods. This project is intended to address the mathematical aspects of numerical approximations of SPDES, including error analysis and complexity analysis and development of new efficient numerical algorithms.