414 overload) for short-horizon operational support [5]. Overall, multihorizon forecasting with uncertainty that can be directly used to compare alternatives (what-if) remains less common in published SAG twins. We address this gap with a probabilistic deep-learning digital twin that separates state representation from action-conditioned dynamics. A convolutional variational autoencoder (CVAE) learns a compact latent state from multivariate observation windows, and a mixture-density recurrent neural network (MDN-RNN) predicts the latent evolution conditioned on recent history and setpoints, providing uncertainty via mixture outputs. The paper focuses on multihorizon forecasting (5–30 min) and what-if evaluation; integration with expert logic, closed-loop predictive control, and reinforcement-learning-based recommendations is left for future work. 2. RELATED WORK Data-driven modeling of SAG mills has been studied with neural networks and other ML methods for short-term forecasting and operational support. Prior work emphasizes process non-stationarity due to ore and regime changes, including approaches to characterize operating regions [8] and comparative analyses of throughput prediction models in SAG circuits [6]. Industrial solutions also combine multi-sensor data with ML for optimization and decision support, though public descriptions often frame them as largely deterministic tools [7]. A representative SAG digital-twin framework under expert control integrates a recurrent/NARXtype model in a closed-loop architecture and incorporates disturbance detection with retraining to cope with changing correlations [4]. Related efforts focus on anticipating critical conditions such as overload rather than multivariable what-if evaluation [5]. Despite its importance for risk-aware decision making, explicit uncertainty quantification is still less common in published SAG twins, compared with broader ML-based industrial digital-twin literature [9]. Methodologically, probabilistic forecasting can be posed as predicting conditional distributions instead of point estimates. MDNs provide a principled mechanism to capture multimodality and heteroscedasticity via input-conditioned mixtures [2], while VAEs/CVAEs learn compact latent representations by optimizing an ELBO (β-ELBO when weighting the KL term) [1]. Inspired by the “representation → dynamics” paradigm of world models [3], this work combines a CVAE for latent-state learning with an MDN-RNN for action-conditioned latent dynamics, enabling probabilistic multihorizon forecasting and what-if analysis for a SAG mill. 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,
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