The identification of initial condition from measurements at a given time is a hard inverse problem, and it can be applied to evaluate the robustness of inversion strategies. Relevant scientific issues are related with estimation of initial condition: cosmology and data assimilation are good examples. Two different inversion methods are employed to identify initial condition for parabolic and hyperbolic differential equations: Genetic Algorithm and Variational Method. The heat transfer process was selected to be used in our tests. A harder inversion is verified on hyperbolic case. Both inverse methods were effective: the numerical difference between the inverse solution was not significant, although the variational method presented a smoother inversion. The inversion obtained with the variational method presented lower processing time.
initial condition identification; epidemic genetic algorithm; variational method; parabolic and hyperbolic differential equation
