Sparse neural networks with skip-connections for identification of aluminum electrolysis cell

Neural networks are rapidly gaining interest in nonlinear system identification due to the model's ability to capture complex input-output relations directly from data. However, despite the flexibility of the approach, there are still concerns about the safety of these models in this context, as well as the need for large amounts of potentially expensive data. Aluminum electrolysis is a highly nonlinear production process, and most of the data must be sampled manually, making the sampling process expensive and infrequent. In the case of infrequent measurements of state variables, the accuracy and open-loop stability of the long-term predictions become highly important. Standard neural networks struggle to provide stable long-term predictions with limited training data. In this work, we investigate the effect of combining concatenated skip-connections and the sparsity-promoting $\ell_1$ regularization on the open-loop stability and accuracy of forecasts with short, medium, and long prediction horizons. The case study is conducted on a high-dimensional and nonlinear simulator representing an aluminum electrolysis cell's mass and energy balance. The proposed model structure contains concatenated skip connections from the input layer and all intermittent layers to the output layer, referred to as InputSkip. $\ell_1$ regularized InputSkip is called sparse InputSkip. The results show that sparse InputSkip outperforms dense and sparse standard feedforward neural networks and dense InputSkip regarding open-loop stability and long-term predictive accuracy. The results are significant when models are trained on datasets of all sizes (small, medium, and large training sets) and for all prediction horizons (short, medium, and long prediction horizons.)