A combined modeling method for complex multi-fidelity data fusion

Abstract Currently, mainstream methods for multi-fidelity data fusion have achieved great success in many fields, but they generally suffer from poor scalability. Therefore, this paper proposes a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:math> combination modeling method for complex multi-fidelity data fusion, devoted to solving the modeling problems with three types of multi-fidelity data fusion, and explores a general solution for any n types of multi-fidelity data fusion. Different from the traditional direct modeling method—Multi-Fidelity Deep Neural Network (MFDNN)—the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:math> method is an indirect modeling method. The experimental results on three representative benchmark functions and the prediction tasks of SG6043 airfoil aerodynamic performance show that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:math> combination modeling has the following advantages: (1) It can quickly establish the mapping relationship between high, medium, and low fidelity data. (2) It can effectively solve the data imbalance problem in multi-fidelity modeling. (3) Compared with MFDNN, it has stronger noise resistance and higher prediction accuracy. Additionally, this paper discusses the scalability problem of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>C</mml:mi> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:mrow> </mml:math> method when n = 4 and n = 5, providing a reference for further research on the combined modeling method.