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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

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

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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