Partially-connected recurrent neural network model generalization error: Application to model predictive control of nonlinear processes

In recent years, modeling of nonlinear systems has increasingly involved machine learning (ML). Recurrent neural networks (RNNs), a type of supervised learning technique, have shown to be effective in modeling time series data. Particularly, it has been demonstrated in several works that physics-informed RNN models (where the network structure is informed by the pattern of interactions of physical process variables) are preferable to dense RNN models. Motivated by this, the present work focuses on the generalization error of partially-connected RNN models and its relationship to the corresponding error of fully-connected RNN models for the same training and testing data sets. The RNN models are subsequently used in model predictive control of nonlinear processes. It is found that the generalization error bounds for the partially-connected RNN models are lower than that of the fully-connected RNN models, and a comparison study using a chemical process example is conducted to demonstrate these results.