## Applied Mathematics Colloquium: Dr. Ting Wang

#### U.S. Army Research Laboratory

Friday, May 3, 2019 · 2 - 3 PM

**Title:**Parametric uncertainty quantification for complex systems

**Speaker: **Ting Wang, U.S. Army Research Laboratory

**Abstract:**Parametric uncertainty quantification (gradient based sensitivity analysis) is an important ingredient in control and optimization of complex systems. In this talk, we consider the steady-state parametric uncertainty quantification of complex systems that can be modeled by a non-steady-state non-equilibrium Markov process. Examples of such complex systems include stochastic reaction networks and molecular dynamics systems. We describe a two-step strategy for estimating the steady-state sensitivity indices of a large-scale system. In the first step, we utilize a tight gradient free upper bound to screen out those insensitive indices, which leads to a dimension reduction in the parameter space. In the second step, we apply the likelihood ratio (LR) scheme to estimate the remaining indices. We show that the centered LR estimators always have constant variances in system time meaning they are particularly efficient in estimating steady-state quantities of a non-steady-state system. Time permitting we discuss some recent results on the second order LR scheme. Application of this strategy in stochastic reaction systems will be demonstrated. Joint work with P. Plechac and G. Stoltz.