A novel hybrid neural network for modeling dynamic systems using physics-informed regularization

Physics-Informed Neural Networks (PINNs) are very popular due to their ability to incorporate first-principles knowledge in traditional neural network models. However, many applications of traditional PINNs in chemical process modeling treat time as an explicit input, rendering them incompatible with a process control framework. In contrast, more advanced approaches for modeling dynamic systems with process control in mind, such as Physics-Informed Recurrent Neural Networks (PI-RNNs), demand high computational resources for both training and implementation. As a solution, we propose a hybrid Physics-Informed Nonlinear Auto-Regressive with eXogenous inputs (PI-NARX) model that is accurate, computationally efficient, and inherits the desired properties of hybrid models. We demonstrate the effectiveness of this approach with a case study based on a Continuous Stirred Tank Reactor. The proposed hybrid model reduces the Mean Absolute Error by 17% for interpolation and 19.5% for extrapolation over the traditional data-driven NARX model. Additionally, we demonstrate the enhanced performance of PI-NARX over NARX in cases of practical importance, such as when limited data or limited process knowledge is available, and in the presence of noisy measurements, indicating the practicality and effectiveness of hybrid machine learning for real-world systems. We also benchmark the performance of the PI-NARX model against that of a PI-RNN, and demonstrate that the PI-NARX model outperforms the PI-RNN in terms of computational efficiency and prediction accuracy.