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Session 36 - Solar Activity.
Display session, Tuesday, June 11
Genetic algorithms are efficient and flexible means of attacking optimization problems that would otherwise be computationally prohibitive. Consider a model that represents an observable quantity in terms of a few parameters, with an associated \chi^2 measuring goodness of fit with respect to data. If the modeled observable is non-linear in the parameters, there can exist a degeneracy of minimum \chi^2 in parameter space. It is then essential to understand the location and extent of this degeneracy in order to find the global optimum and quantify the degeneracy error around it. Traditional methods of spanning parameter space such as a grid search or a Monte Carlo approach scale exponentially with the number of parameters, and waste a great deal of computational time looking at ``un-fit'' solutions. Genetic algorithms, on the other hand, converge rapidly onto regions of minimum \chi^2 while continuously generate ``mutant solutions'', allowing an efficient and comprehensive exploration of parameter space. Our aim has been to develop an approach that simultaneously yields a best fit solution and global error estimates, by modifying and extending standard genetic algorithm-based techniques.
We fit two magnetostatic models of the solar minimum corona to observations in white light. The first model allows horizontal bulk currents and the second also allows sheet currents enclosing and extending out from the equatorial helmet streamer. Using our genetic algorithm approach, we map out the degeneracy of model parameters that reproduce observations well. The flexibility of genetic algorithms facilitates incorporating the additional observational constraint of photospheric magnetic flux, reducing the degeneracy of solutions to a range represented by reasonable error bars on the model predictions. By using genetic algorithms we are able to identify and constrain the degeneracy inherent to the models, a task, which, particularly for the more complex second model, would be impractical using a traditional technique. The ultimate result is a greater understanding of the large scale structure of the solar corona, providing clues to the mechanisms heating the corona and accelerating the solar wind.
Program listing for Tuesday