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Vectorial modeling concept is proposed in this paper by introducing the matrix theory into the point modeling concept (surrogate modeling strategy), and an adaptive vectorial surrogate modeling framework (AVSMF, short for) is developed based on the vectorial modeling concept and adaptive modeling strategy. Herein, the adaptive modeling strategy is adopted to determine the form of mathematical model of each objective in line with the cost function, the surrogate modeling strategy is regarded as the basis function for reflecting the relationship of the output of single-objective between the relevant inputs, and the matrix theory is used to ascertain the vectors and cell arrays of undetermined parameters and to establish the performance function of multi-objective structures. To validate the proposed method, we use three examples including approximate and probabilistic analysis of nonlinear function with multiple …