Colloquium - 3/04, 3:00PM, Duncan Hall 1064

Matthias Heinkenschloss

Department of Computational and Applied
Rice University

"A New Approach for Model and Parameter Identification"

I discuss an approach to discriminate between a finite number of parameter-dependent mathematical models from experiments. This research is motivated by the need to select from several possible constitutive equations the one that models the material behavior. To determine the "true" constitutive equation as well as the parameters in it, one can conduct experiments, e.g., apply forces and measure displacements. The question is what experiments to perform and how to use them to identity the model.

The proposed approach first determines experiments that best discriminate between models. Then experiments are conducted and based on the outcome of the experiments the "true" model is identified. Sufficient conditions to discriminate between models are given. Once the model is identified, additional experiments are performed to estimate the parameters in the identified model. Compared to some earlier approaches to discriminate between models the proposed method allows for more general models, requires fewer assumptions, and under suitable conditions is guaranteed to identify the correct model.

The performance of the new approach is illustrated using model problems governed by elliptic partial differential equations and from computational viscoelasticity.

This talk is based on joint work with Markus Bambach and Michael Herty (both RWTH Aachen)