Abstract: Using the Bayesiandifferential evolution algorithm, we discussed the twodimensional heat conduction equation. The inversion estimation of the heat source position was given through the observation temperature at different time of an observation point. The numerical experiment results show that, with the increase of the number of iterations, the error of the position parameter of the heat source decreases. When the number of iterations reaches 120, the relative error of the parameter inversion is controlled within 2%. When 5% and 10% white noise are added to the observed data, the relative error changes little, which indicates that the algorithm has good stability.

Key words: inverse problem, Bayesian theory, differential evolution algorithm, heat source estimation