Parameter estimation for partial differential equations using stochastic methods

摘要

The aim of this thesis is to compare the efficiency of different algorithms on estimating parametersudthat arise in partial differential equations: Kalman Filters (Ensemble Kalman Filter,udStochastic Collocation Kalman Filter, Karhunen-Lo`eve Ensemble Kalman Filter, Karhunen-udLo`eve Stochastic Collocation Kalman Filter), Markov-Chain Monte Carlo sampling schemesudand Adjoint variable-based method.udWe also present the theoretical results for stochastic optimal control for problems constrainedudby partial differential equations with random input data in a mixed finite element form. Weudverify experimentally with numerical simulations using Adjoint variable-based method withudvarious identification objectives that either minimize the expectation of a tracking cost functionaludor minimize the difference of desired statistical quantities in the appropriate Lp norm.