Physics-Informed Neural Networks for Dynamic Process Operations with Limited Physical Knowledge and Data

Mathematical models describing the behavior of such processes can be classified concerning their degree of reliance on physical/chemical knowledge or data into three categories: (1) white-box or first-principle or mechanistic models, (2) black-box or data-driven models, and (3) gray-box or hybrid models (Zendehboudi et al., 2018; Marquardt, 1996). Black-box modeling relies on (measurement) data to establish a predictive relation between process inputs and outputs, thus avoiding the need for a mechanistic process description. In recent years, approaches involving deep neural networks (DNNs) have become particularly prominent data-driven models for process operations. DNNs can model nonlinear dependencies between multiple inputs and outputs (Goodfellow et al., 2016) but require extensive training data and often fail to make physically consistent predictions in scientific or engineering applications (Zendehboudi et al., 2018). In contrast, mechanistic process models are based on the governing physical and chemical laws of a system and comprise relatively few parameters that need to be estimated from data (von Stosch et al., 2014).