{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T19:36:47Z","timestamp":1771961807990,"version":"3.50.1"},"reference-count":48,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,6]],"date-time":"2020-02-06T00:00:00Z","timestamp":1580947200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71673292, 21808181, 61673388, 71673294"],"award-info":[{"award-number":["71673292, 21808181, 61673388, 71673294"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key Research &amp; Development (R&amp;D) Plan","award":["2018YFC0806900"],"award-info":[{"award-number":["2018YFC0806900"]}]},{"name":"National Social Science Foundation of China","award":["17CGL047"],"award-info":[{"award-number":["17CGL047"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/sym12020254","type":"journal-article","created":{"date-parts":[[2020,2,7]],"date-time":"2020-02-07T03:13:27Z","timestamp":1581045207000},"page":"254","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["The Gray-Box Based Modeling Approach Integrating Both Mechanism-Model and Data-Model: The Case of Atmospheric Contaminant Dispersion"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2962-9254","authenticated-orcid":false,"given":"Bin","family":"Chen","sequence":"first","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, 109 Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiduo","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, 109 Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rongxiao","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, 109 Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengqiu","family":"Zhu","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, 109 Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liang","family":"Ma","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, 109 Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaogang","family":"Qiu","sequence":"additional","affiliation":[{"name":"College of Systems Engineering, National University of Defense Technology, 109 Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9426-5303","authenticated-orcid":false,"given":"Weihui","family":"Dai","sequence":"additional","affiliation":[{"name":"School of Management, Fudan University, Shanghai 200433, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,6]]},"reference":[{"key":"ref_1","first-page":"2064","article-title":"An Intelligent ACP based Experimental Approach","volume":"29","author":"Chen","year":"2017","journal-title":"J. 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