431 As machine learning became integrated into predictive grinding models, Both and Dimitrakopoulos (2021) demonstrated that neural networks can capture nonlinear relationships between mill power, ore hardness, and throughput, with P80 used as a predictor variable. Their formulation addresses the inverse of the problem treated here, where P80 is the output to be forecast from operational inputs and its focus on longterm performance rather than short-horizon dynamics underscores the need for approaches designed specifically for real-time P80 prediction. Saldaña et al. (2023) extended this line of work to SAG mill optimization using Random Forest, XGBoost, and neural networks, achieving up to R² = 0.89. However, these non-temporal models operate on process snapshots and are structurally incapable of exploiting the strong autocorrelation of P80 at short sampling intervals, a fundamental limitation that motivates the adoption of recurrent neural networks. Zeb et al. (2024) demonstrated that LSTM networks achieve accurate short-horizon forecasts of dynamic metallurgical variables (specifically flotation concentrate grade) in multivariate industrial timeseries over windows up to 30 minutes. The temporal dependencies governing concentrate grade are structurally analogous to those of P80 in a closed circuit, providing direct methodological justification for the autoregressive LSTM design adopted here, in which the lagged P80 value is included as an additional input feature. Quintanilla et al. (2024) developed the closest existing architecture to the present framework: a digital twin coupling a recurrent neural network surrogate with a real-time control system for a closed SAG mill circuit. The key distinctions are that their control policy is rule-based rather than learned, P80 is not the primary forecasting target, and the control problem is not formulated as a sequential decision-making task. Nian et al. (2020) established reinforcement learning as a principled paradigm for industrial process control, identifying online exploration cost as the central practical barrier and motivating offline RL from historical data. Moerland et al. (2023) further demonstrated that differentiable learned surrogates can serve as transition models for policy gradient training, enabling backpropagation through the surrogate without any real plant interaction. While prior works have demonstrated the value of machine learning and intelligent optimization for improving mill performance, no previous study has addressed the combined problem of forecasting P80 as a dynamic autoregressive time-series variable using LSTM networks and using the resulting surrogate model as the environment for an offline RL control agent trained from historical plant data. In this context, Long Short-Term Memory networks are adopted due to their ability to capture temporal dependencies and nonlinear behavior inherent to grinding processes. The proposed approach not only enables accurate shortterm P80 prediction, but also establishes a differentiable surrogate environment that directly supports the offline reinforcement learning formulation developed in this work, in which the trained LSTM serves as the transition model for policy optimization without requiring online plant experimentation. 3. METHODOLOGY This paper proposes a data-driven methodology for short-term P80 control in an industrial grinding circuit, based on multivariate time-series modeling using LSTM forecasting networks as a high-fidelity surrogate environment with offline Reinforcement Learning (RL) to enable predictive and P80 control. Four LSTM architectures are systematically compared (a baseline exogenous formulation and a featureengineered variant incorporating metallurgical priors) and two autoregressive models (a formulation with lagged P80 feedback and a hybrid combining both strategies). Offline RL strategy is then evaluated following the process variable taxonomy of Hodouin (2011), this is a model-based differentiable actor-critic. 3.1. Data Preprocessing Data preprocessing was applied consistently across all four architectures. Raw 1-second sensor data were cleaned against operational limits (validated in collaboration with experienced metallurgists to retain only physically meaningful observations) and aggregated to 5-minute intervals via mean downsampling, preserving process dynamics while reducing computational burden. Temporal integrity was enforced through strict datetime index validation. A chronological 70/15/15 train/validation/test split was applied to preserve causal structure and prevent information leakage. Independent Minmax scalers were fitted exclusively on the training partition and subsequently applied to validation and test sets, mapping each feature to [0, 1];
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