An integrated framework for co-simulation of white-box models and black-box models

  • Wenjia Zhang,
  • Wenzheng Liu,
  • Heming Zhang 
  • a,b University of Pardubice, Faculty of Transport Engineering, Studentská 95, CZ-532 10, Pardubice, Czech Republic
Cite as
Zhang W., (b)Wenzheng Liu, (c)Heming Zhang (2021). An integrated framework for co-simulation of
white-box models and black-box models. Proceedings of the 33rd European Modeling & Simulation Symposium (EMSS 2021), pp. 84-89. DOI:


Integration of heterogeneous models can achieve interconnection between multiple types of simulation systems and realize reusability of model components. Recently data-driven modeling is becoming more and more common with the popularity of machine learning. It is a representative of black-box models which are totally dependent on data and need no disciplinary knowledge. From this perspective, models can be divided into white-box models, grey-box models and black-box models. Few researchers have considered the integrated issue under this mode. In this paper, we propose an integrated framework for scenarios where white-box models and black-box models are both involved. We discuss the structures of corresponding proxy models and then introduce a modified advancing strategy for general optimistic methods. It can greatly avoid possible rollback for black-box models and achieve efficient simulation by adjustment of simulation sequence.


  1. Beghi, A., Liberati, M., Mezzalira, S., and Peron, S. (2007). Grey-box modeling of a motorcycle shock absorber for virtual prototyping applications. Simu lation Modelling Practice and Theory, 15(8):894–907. 
  2. Dolk, D. R. and Kottemann, J. E. (1993). Model integra tion and a theory of models. Decision Support Systems, 9(1):51–63. 
  3. Duun-Henriksen, A. K., Schmidt, S., Roge, R. M., Moller, J. B., Norgaard, K., Jorgensen, J. B., and Mad sen, H. (2013). Model identification using stochastic differential equation grey-box models in diabetes. Journal of diabetes science and technology, 7(2):431– 440. 
  4. Garcia, J. D., Prada, L., Fernandez, J., and Nunez, A. (2008). Using black-box modeling techniques for modern disk drives service time simulation. IEEE. 
  5. Jefferson, D. R. (1985). Virtual time. ACM Trans. Pro gram. Lang. Syst., 7(3):404–425. 
  6. K.Venkatesh, T.Radhakrishnan, H. (1986). Discrete event simulation in a distributed system. IEEE Computer Society Press. 
  7. Kübler, R. and Schiehlen, W. (2000). Two methods of simulator coupling. Mathematical and Computer Modelling of Dynamical Systems, 6(2):93–113. 
  8. Leifsson, L. T., S?Varsdóttir, H., Siguresson, S. T., and Vésteinsson, A. (2008). Grey-box modeling of an ocean vessel for operational optimization. Simulation Modelling Practice Theory, 16(8):923–932. 
  9. Liang, S., Zhang, H., and Wang (2011). Combina tive algorithms for the multidisciplinary collabora tive simulation of complex mechatronic products based on major step and convergent integration step. CHINESE JOURNAL OF MECHANICAL ENGINEER ING -ENGLISH EDITION-. 
  10. Liang, S. (2009). Research on multidisciplinary collabo rative simulation algorithm for complex product. PhD thesis, Tsinghua University. 
  11. Lin, Y. (2006). Research and implementation on collabo rative simulation technology based on HLA. PhD thesis, Tsinghua University. 
  12. Lubachevsky, B. D. (1989). Efficient distributed event driven simulations of multiple-loop networks. Com munications of the ACM. 
  13. Sokol, L. M., Weissman, J. B., and Mutchler, P. A. (1991). Mtw: an empirical performance study. In 1991 Winter Simulation Conference Proceedings., pages 557–563.