A Multiobjective Evolutionary Algorithm for Numerical Parameter Space Characterization of Reaction Diffusion Systems

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Abstract

Mathematical modeling is used to assist in studying complex biological systems. Still, setting up and characterizing models pose challenges of its own: identifying suitable model parameters, even when high-resolution time course data concerning the system behavior is available, is a difficult task. This task is further complicated when this high-resolution data remains unavailable like for the tissue level systems considered in developmental biology—a type of systems we focus on in the present study. In addition, costly simulations for tissue level systems prohibit excessive simulations during the parameter estimation phase.

Here, we propose an approach that is dedicated to assist in the task of parameter space characterization for reaction diffusion models—a common type of models in developmental biology. We investigate a method to numerically identify boundaries that partition the parameter space of a given model in regions that result in qualitatively different system behavior. Using an Evolutionary Algorithm (EA) combined with an Artificial Neural Network (ANN), we try to identify a representative set of parameter settings minimizing the distance to such boundaries. In detail we train the ANN on numerical data annotated using analytical results to learn the mapping between parameter space and distances to boundaries, thereby guiding the optimization process of the EA to identify such a set of parameter settings. The approach is tested with respect to its boundary identification and generalization capabilities on three different reaction diffusion systems—for all three we are capable of reliably identifying boundaries using the proposed approach.