How to Be a Gray Box: The Art of Dynamic Semi-Physical Modeling

Yacine Oussar (1) , Gérard Dreyfus (1)

1 SIGMA - Laboratoire Signaux, Modèles et Apprentissage Statistique

A general methodology for gray-box, or semi-physical, modeling is presented. This technique is intended to combine the best of two worlds: knowledge-based modeling, whereby mathematical equations are derived in order to describe a process, based on a physical (or chemical, biological, etc.) analysis, and black-box modeling, whereby a parameterized model is designed, whose parameters are estimated solely from measurements made on the process. The gray-box modeling technique is very valuable whenever a knowledge-based model exists, but is not fully satisfactory and cannot be improved by further analysis (or can only be improved at a very large computational cost). We describe the design methodology of a gray-box model, and illustrate it on a didactic example. We emphasize the importance of the choice of the discretization scheme used for transforming the differential equations of the knowledge- based model into a set of discrete-time recurrent equations. Finally, an application to a real, complex industrial process is presented.

Domaines: Apprentissage [cs.LG]; Machine Learning [stat.ML]; Réseau de neurones [cs.NE]

Yacine Oussar, Gérard Dreyfus. How to Be a Gray Box: The Art of Dynamic Semi-Physical Modeling. Neural Networks, 2001, 14 (1), pp.1161-1172. ⟨hal-00922197⟩