1. INTRODUCTION Grinding circuits are among the highest energy-consuming and economically critical units in concentrator plants. In particular, SAG mills exhibit strong nonlinearities, multivariable coupling, and time-varying behavior driven by ore variability, liner wear, and downstream constraints. Operationally, the key objective is to maximize (or sustain) throughput while respecting limits on pressure, power, pebble load, impacts, and product size distribution; however, the feasible optimum shifts as ore and plant conditions evolve. Decision support is often built on deterministic, offline models (e.g., operating envelopes or expert-system tuning). When deployed online, these models can degrade because they learn regime-specific correlations. Prior work on NARX-based SAG digital twins reports horizondependent error growth due to autoregression and the practical need for smoothing, disturbance detection, and retraining to maintain performance under changing conditions [4]. Other approaches target critical-condition prediction (e.g., 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 mixturedensity 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, closedloop 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 nonstationarity 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/NARX-type 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.
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