Figure 3 – Multi-step forecasting setup showing a 30-minute lookback window and two-step P80 prediction horizon. 3.3. LSTM Forecasting: models, architecture and training Four distinct LSTM models were evaluated: Baseline, Feature Engineering, Autoregressive, and Hybrid, categorized by their integration of temporal feedback loops and domain-specific metallurgical knowledge. Model 1 (Baseline) utilizes nine original operational variables to establish a direct sensor-to-output mapping. Model 2 (Feature Engineering) expands the input space to 17 features by integrating derived variables, testing the hypothesis that explicit physical laws improve predictive stability. A critical distinction is made between nonautoregressive models (1 and 2), which must infer P80 dynamics indirectly from process states, and autoregressive models (3 and 4), which incorporate lagged P80 values within the look-back window. While Model 3 focuses exclusively on this temporal lag structure, Model 4 (Hybrid) leverages a synergistic approach, combining all 17 engineered and lagged features to capture both recent particle size trends and fundamental grinding principles. A progressive comparison strategy was adopted, ensuring all models were trained under identical preprocessing and environmental conditions to facilitate an unbiased evaluation of different modeling assumptions. All four variants share a standardized stacked-LSTM backbone, consisting of two recurrent layers followed by a linear dense output, as detailed in Table 1. This hierarchical structure is designed to extract high-level temporal features in the first layer and map them to the output horizon in the second. Table 1 – Common LSTM Architecture for all proposed forecasting models. Parameter Specification Input layer 3D Tensor (Batch, 6 Timesteps, N Features) Hidden Layer 1 LSTM (64 units), activation='tanh', return_sequences=True Regularization 1 Dropout (20%) Hidden Layer 2 LSTM (32 units), activation='tanh', return_sequences=False Regularization Dropout (20%)
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