Approximation of a multidimensional dependency based on linear expansion in a dictionary of parametric functions

The problem of a multidimensional function approximation using a finite set of pairs “point” – “function value at this point” is considered. As a model for the function, an expansion in a dictionary containing nonlinear parametric functions has been used. Several subproblems should be solved when constructing an approximation based on such model: extraction of a validation sample, initialization of parameters of the functions from the dictionary, and tuning of these parameters. Efficient methods for solving these subproblems have been suggested. Efficiency of the proposed approach is demonstrated on some problems of engineering design.