Physics Constrained Learning in Neural Network based Modeling

Abstract

Neural Network (NN) models based on training solely using data are limited in their use due to issues related to extrapolability and interpretability. On the other hand, while mechanistic models based on governing physical laws can overcome these limitations, the unavailability of accurate mechanistic models render them unsuitable for critical applications. In this paper, we propose an approach to develop an NN model that is trained to exploit available data while also being regularized by physics based information; in other words the loss function of NN is augmented by constraints associated with the system physics. This approach, also known as PINNs (Raissi et al. 2019) has been applied to representative problems in process systems engineering (PSE) to evaluate its efficacy to represent the knowledge about the physics of the system while also exploiting the information in the data. It has been shown that in the presence of noisy data and partially known physics model, this approach can give better predictions compared to the conventional training methodology. It has also been shown that the constraints given by the physics based model are also satisfied to a greater extent as compared to models trained only on data.