Mathematical Sciences: Numerical Methods for Parameter Estimation in Distributed Parameter Systems

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This project undertakes research on numerical methods for parameter estimation in distributed parameter systems. Several important topics are addressed. Parameter estimation problems are typically formulated as optimization problems, which are solved using gradient methods. The first topic is the efficient computation of gradients using costate methods coupled with time-Galerkin methods. The second topic is the choice of regularization (i.e., stabilization) parameters in the optimization formulation. Related to this is the topic of choosing system inputs and observations to maximize information content. These numerical methods are used to develop computer models that describe ion flow in instruments used in analytical chemistry. These techniques may also be applied to a broad range of disciplines that use mathematical models to describe similar phenomena. Examples include the modelling of flow through porous media, which has important applications in the cleanup of polluted groundwater and in enhanced oil recovery.