432 separate scalers were retained for input variables and the target P80. All scaler objects are saved alongside the model weights to ensure consistent preprocessing at inference time in the RL environment 3.2. Sequence Construction All four LSTM variants employ a sliding-window encoder that transforms the univariate-indexed time series into a supervised three-dimensional tensor. A lookback window of W = 6 timesteps (representing 30 minutes of historical context) is used to predict a forecast horizon of H = 2 timesteps (10 minutes ahead). This horizon was specifically designed to approximate ball mill residence time dynamics. The resulting tensor structures are X ∈ RN ×6×F and y ∈ RN ×2×1, where F denotes the number of input features (which varies by model configuration) and N = T − W − H + 1 represents the number of valid windows after boundary trimming. The trailing singleton dimension in y explicitly encodes the univariate nature of the target variable (P80), maintaining dimensional consistency with deep learning frameworks where the final axis corresponds to feature channels. Figure 3 illustrates the use of a sliding window approach to create input/output pairs for the LSTM, non-autoregressive variants exclude P80 from the input window; autoregressive variants include lagged P80 as an additional input covariate. 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-tooutput 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 non-autoregressive 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.
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