Abstract: Kriging surrogate can be used to identify the parameters for the mathematical models described by ordinary differential equations. By training a relatively small set of samples, Kriging surrogate can partially replace the time-consuming original objective function optimization process, so it can save a lot of computation time. And the optimization algorithm of searching new samples has major impacts on result of the parameter estimation during the process of refining Kriging surrogate models. For the problem of parameters estimation described by ordinary differential equations with nonlinearity and sloppiness, this paper combines the advantages of Adam with second order momentum and SGD with momentum to search for new sample points that need to be added during model refinement, so as to improve the convergence speed and search quality. Compared with other optimization algorithms, the effectiveness of the proposed algorithm is verified.

Key words: combinatorial optimization, parameter estimation, Kriging surrogate model