Evolutionary algorithm for parameter identification inverse problems in parabolic systems

We study a general evolutionary methodology for parameter identification problems in parabolic systems. Using EAs (evolutionary algorithms) avoids some of the weaknesses of traditional gradient-based analytical search methods including the difficulty in constructing well-defined mathematical models directly from the practical inverse problem, and easily getting trapped or oscillating between local minima and thus failing to produce useful solutions. An evolutionary algorithm for constructing a spatially varying diffusion parameter from observed data is proposed. By spline theory, we approximate the infinite dimensional inverse problem by a problem in the finite dimensional space. Numerical experiments are presented to illustrate the efficiency of the proposed approach.