With the profound understanding of the world, modeling and simulation has been used to solve the problems of complex systems. Generally, mechanism-models are often used to model the engineering systems following the Newton laws, and this kind of modeling approach is called white-box modeling; however, when the internal structure and characteristics of some systems are hard to understand, the black-box modeling based on statistic and data-modeling is often used. For most complex real systems, a single modeling approach can hardly describe the target system accurately. In this paper, we firstly discuss and compare the white-box and black-box modeling approaches. Then, to mitigate the limitations of these two modeling methods in mechanism-partially-observed systems, the gray-box based modeling approach integrating both a mechanism model and data model is proposed. In order to explain the idea of gray-box based modeling, the atmosphere dispersion modeling is studied in practical cases from two symmetric aspects. Specifically, the framework of data assimilation is used to illustrate the modeling from white-box to gray-box, while the Gauss features based Support Vector Regression (SVR) models are used to illustrate the modeling from black-box to gray-box. To verify the feasibility of the gray-box modeling method, we conducted both simulation experiments and real dataset symmetry experiments. The experiment results show the enhanced performance of the gray-box based modeling approach. In the end, we expect that this gray-box based modeling approach will be an alternative modeling approach for different existing systems.
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