LANS Informal Seminar: Hong Zhang

Seminar Title: Sensitivity analysis of time-dependent simulations
Speaker: Hong Zhang, Postdoctoral Appointee, MCS, Argonne National Laboratory

Date/Time: 2015-06-10 15:00
Location: Building 240, Room 1404-1405

Description:
Sensitivity analysis is crucial to identify the most influential parameters in simulations, to study the behavior of models, and to solve dynamic constrained optimization problems. It has been recognized as an indispensable technique in uncertainty quantification and inverse problems.

Traditional Automatic Differentiation (AD) technique can evaluate the sensitivity for an arbitrary sequence of computer codes. It is possible to consider our approaches for sensitivity analysis as AD at a different level of abstraction. The time-dependent simulation is composed of a sequence of time steps; at each time step, the numerical solution is propagated with certain time stepping algorithm such as Euler methods and Runge-Kutta methods. Therefore, the sensitivity model, derived in a discretize-then-differentiate manner, is essentially an AD process on a sequence of primitive operations at the time stepping level.

In this talk, I will present the forward and discrete adjoint sensitivity analysis components in PETSc, which, together with some examples, will be released just around the corner. Specifically, I will address how to choose between different approaches for efficiency, how the algorithms are derived and implemented, how to compute the sensitivities for hybrid systems where there are state-dependent jumps, and demonstrate their use in power system as an application example. But many other applications, especially existing ones using PETSc, would also be expected to benefit from this development without too much effort on the user’s part.