Abstract: In this paper, the inverse problem of the 2-D steady heat conduction is investigated. Firstly, the training points set is allocated. Then, the approximate solution of the problem is expressed as the form of the combination of the Gauss kernel functions which related to the training points. Moreover, the parameters are optimized basing on the least squares support vector machines. The approximate solution consists of two parts. The first part is a known function that satisfies the boundary condition, and the other part is the combination of Gauss Kernel functions which including regression coefficients. Finally, the validity of the proposed method is verified by two examples which have analytical solutions. The result shows that the proposed method is feasible to solve the inverse problem of the 2-D steady heat conduction.

Key words: steady heat conduction, heat source inverse problem, least square support vector machine, quadratic programming, approximate solutions