A hybrid modelling approach to model process dynamics by the discovery of a system of partial differential equations

The development of first principle based models for some complex processes might not be feasible due to computational cost or insufficient information. The sparse optimization approach is prominently utilized to obtain data-driven models using spatiotemporal data for such processes. The models developed assume either complete or no knowledge about the structure of the partial differential equation (PDE). However, we can exploit the process knowledge or the basic governing laws to infer the partial structure of the PDE prior to the data-driven modeling. This paper proposes a hybrid modeling approach to obtain the underlying PDE system by integrating partial knowledge of the system into data-driven modeling. We also infer the optimal gradient estimation method for handling different levels of noise in the data. Finally, three complex systems of PDEs discovered using the hybrid modeling approach are presented as case studies to illustrate the advantage of hybrid modeling over purely data-driven modeling.(c) 2022 Elsevier Ltd. All rights reserved.