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Neural networks are rapidly gaining interest in nonlinear systemidentification due to the model's ability to capture complex input-outputrelations directly from data. However, despite the flexibility of the approach,there are still concerns about the safety of these models in this context, aswell as the need for large amounts of potentially expensive data. Aluminumelectrolysis is a highly nonlinear production process, and most of the datamust be sampled manually, making the sampling process expensive and infrequent.In the case of infrequent measurements of state variables, the accuracy andopen-loop stability of the long-term predictions become highly important.Standard neural networks struggle to provide stable long-term predictions withlimited training data. In this work, we investigate the effect of combiningconcatenated 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 ahigh-dimensional and nonlinear simulator representing an aluminum electrolysiscell's mass and energy balance. The proposed model structure containsconcatenated skip connections from the input layer and all intermittent layersto the output layer, referred to as InputSkip. $\ell_1$ regularized InputSkipis called sparse InputSkip. The results show that sparse InputSkip outperformsdense and sparse standard feedforward neural networks and dense InputSkipregarding open-loop stability and long-term predictive accuracy. The resultsare 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.)

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