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Talk Abstract
The Search for Control Parameters of a Nonlinear Partial Differential Equation: The Good News, the Bad News, and a Success Story

Rogene M. Eichler West, University of Minnesota

Many physical systems of interest to scientists and engineers can be modeled using a partial differential equation extended along the dimensions of time and space. These equations are typically non-linear with real-valued parameters that control the classes of behaviors that the model is able to produce. Unfortunately, these control parameters are often difficult to measure in the physical system. Consequently, the first role of modeling is often to search for appropriate parameter values. In a high-dimensional system, this task potentially requires a prohibitive number of evaluations.

We have applied evolutionary algorithms to the problem of parameter selection in models of biologically realistic neurons. Unlike most EA applications, we designed our fitness measure to take into account the noisy nature of experimental data such as that obtained from biological systems. Further, our objective was not to find the ``best" solution, but rather we sought to produce the manifold of high fitness solutions that best accounts for biological variability. The search space was high dimensional (> 100) and each function evaluation required from one minute to one hour of CPU time on high-performance computers. Using this model and our goals as an example, the content of this talk will: (1) review strategies used for real-valued representations both from the literature and from our applications; (2) discuss the difficulties in developing an adequate fitness measure to match and reward simulated data compared to noisy experimental data; (3) examine the role of representation in determining the difficulty of search; and (4) provide some options for parallelizing search on high-performance computing platforms.

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1996-1997 Mathematics in High Performance Computing

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