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SSC Seminar Series - Mark Girolami

Friday, March 28, 2014, 02:00pm - 03:00pm

Title: Defining Posterior Measures on the Hilbert Space of Differential Equation Solutions.

Abstract: Solving the forward and inverse problems when quantifying uncertainty in models of physical systems described by ordinary and partial differential equations requires a coherent probabilistic framework. Quantifying sources of uncertainty in the forward problem must include the non-analytic nature of solutions of ODE and PDEs which in all but the simplest cases demands finite dimensional functional approximations e.g. Finite elements, and discrete time numerical integration. The epistemic nature of this uncertainty can be formally defined by imposing appropriate prior measures on the Hilbert space of vector fields and corresponding solutions via the Radon-Nikodyn derivative leading to continuous posterior measures over solutions. This work describes such methods to probabilistically solve ODE and PDEs with proofs of consistency provided. Examples will include UQ for Navier-Stokes equations, chaotic PDEs (Kuramoto-Shivasinsky), and biochemical kinetics.

Location : CBA 4.330
Contact : Sasha Schellenberg