Fokker-planck Equations: Uncertainty in Network Security Games and Information

We have significant accomplishments on uncertainty quantification in inverse problems for dynamical systems, generalized sensitivity and optimal design of experiments, elasticity and viscoelasticity modeling for buried target detection, and general inverse problem methodology for proliferating populations. Our efforts have continued on development of efficient accurate integration of Fokker Planck equations. Our objective is to analyze and optimize the dynamic behavior of nonlinear stochastic differential equations, especially the stochastic resonance effects based on the probability density function generated by the Fokker Planck equation. Our approach uses the backward characteristic method and the time-splitting integration of the Fokker Planck equation. Status/Progress 1. Development of innovative computational approaches for general classes of FokkerPlanck systems and uncertainty quantification: Our efforts on developing efficient accurate integration of Fokker Planck equations have continued with success. One objective is to analyze and optimize the dynamic behavior of nonlinear stochastic differential equations, especially the stochastic resonance effects based on the probability density function generated by the Fokker Planck equation. One approach uses the backward characteristic method and the time-splitting integration of the Fokker Planck equation. We use cubic interpolation based on the solution and its derivatives to resolve the required accuracy. Then the solution and its derivatives are simultaneously updated by the backward characteristic method. We have successfully implemented a proposed time-splitting integration of the Fokker Planck equation. The method is very efficient and stable and allows one to have a large time-stepsize. We have used these methods to develop dynamic object identification and stochastic resonance techniques for detecting subliminal objects. In other efforts, we have developed fast computational methods for certain classes of Fokker Planck equations by conversion to an equivalent but simpler first order hyperbolic system with uncertainty in the coefficients which can be correctly