3. PROBLEM DEFINITION AND SCOPE Objective. We develop a plant-grade probabilistic digital twin for a SAG mill to forecast key process variables over 5–30 minutes and to evaluate what-if setpoint changes before execution. Forecasts are expressed as conditional distributions summarized with P10–P90 uncertainty bands to support risk-aware comparisons. Problem setting. At time t, given recent multivariate history of observations, operator setpoints (actions), and exogenous inputs, the model estimates future observations at horizons h∈ {5,15,30}minutes under noisy, correlated, and non-stationary industrial conditions. Scope and out of scope. This paper covers multihorizon forecasting and scenario simulation with uncertainty quantification, including a latent state representation, an action-conditioned dynamics model, and a chronological, deployment-oriented validation protocol. It does not address operator-interface/alarm redesign, closed-loop automatic control, or learning/replicating the plant expert policy; integration with expert logic, MPC, or RL is left for future work. Deployment constraints. The twin is designed for online inference at 1-minute sampling using a sliding-history input (≈30 minutes of context) and supports repeated what-if evaluations from the same operating snapshot. 4. DATA AND PRE-PROCESSING We used 1-minute sampled operational data from the Primary Grinding line, covering stockpile level, apron-feeder participation and size distribution, SAG feed throughput (PV/SP) and feed size fractions, percent solids (PV/SP), inlet water flow, mill speed, power, impact intensity, load width and toe position, filling level, feed/discharge pressures, and pebble tonnage. Signals were grouped into observations (process states/outputs), actions (operator/setpoint variables), and exogenous inputs (short-term non-manipulable conditions). Data were timeordered and preprocessed with (i) optional operating-regime filtering, (ii) outlier clipping, (iii) removal of missing values in critical variables with limited within-segment interpolation (≤1minute gap), and (iv) segmentation into continuous blocks with at least 1 hour of valid data. To avoid temporal leakage, segments were split chronologically into train/validation/test (with a window gap when required). The CVAE was trained only on observation windows to learn a latent process state, and the MDN-RNN was trained to forecast 5/15/30-minute horizons using latent history plus action and exogenous variables. 5. METHOD This section describes the proposed probabilistic digital twin as a representation–dynamics pipeline. First, a convolutional variational autoencoder (CVAE) learns a compact latent state of the SAG milling process from multivariate observation windows. Second, a mixture-density recurrent neural network (MDN-RNN) models the stochastic evolution of this latent state conditioned on recent history, operator actions (setpoints), and exogenous drivers. This separation enables plant-
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