422 percent solids, fill level). In contrast, indicators that are more stochastic or influenced by unobserved factors in the primary grinding line show higher errors; nevertheless, they remain useful for trend monitoring and as part of the latent state that conditions other predictions. Finally, the scope of this paper is multihorizon forecasting and what-if evaluation, not control. However, the results suggest a clear path to integrate the twin with the existing primary grinding expert logic and enable more predictive operation in follow-up work. 8. CONCLUSIONS AND NEXT STEPS This work presented a probabilistic digital twin for primary grinding based on deep learning, designed to deliver multihorizon forecasts (5–30 min) and what-if evaluation with uncertainty quantification through P10–P90 bands. The proposed architecture explicitly separates latent state learning (CVAE) from conditioned dynamics modeling (MDN-RNN), yielding an approach that is robust to noise, collinearity, and the regime variability typical of primary grinding. On unseen data, the model achieves performance suitable for operational decision support across a relevant set of critical variables, with several of them exhibiting MAPE below 10% at industrially meaningful horizons. Moreover, the probabilistic formulation makes it possible to communicate the risk associated with operational changes explicitly, enabling pre-action scenario comparisons (what-if), which is particularly valuable when the process state changes rapidly. Future work is organized along three main directions. First, strengthening deployment aspects: drift monitoring, periodic recalibration, and uncertainty-based operational “confidence” criteria to support control-room usage. Second, coupling the twin with existing expert logic to enable more predictive operation (evaluating alternatives under constraints before executing actions). Third, extending the framework toward recommendation/control via reinforcement learning or optimization-based strategies, using the twin as an environment model to explore policies that maximize throughput while respecting operational constraints and considering downstream impacts. REFERENCES [1] D. P. Kingma and M. Welling, "Auto-Encoding Variational Bayes," arXiv:1312.6114, 2013. [2] C. M. Bishop, "Mixture Density Networks," Aston University, NCRG/94/004, 1994. [3] D. Ha and J. Schmidhuber, "World Models," arXiv:1803.10122, 2018. [4] P. Quintanilla, F. Fernandez, C. Mancilla, M. Rojas, M. Estrada and D. Navia, " Digital twin with automatic disturbance detection for an expert-controlled SAG mill," Minerals Engineering, 220, 109076, 2024. [5] R. Hermosilla, C. Valle, H. Allende, E. Lucic and P. Espinoza, “Semi-Autogenous (SAG) Mill Overload Forecasting,” in Pattern Recognition and Image Analysis (CIARP 2021), Lecture Notes in Computer Science, vol. 12702, J. M. R. S. Tavares et al. (Eds.), Springer Nature Switzerland AG, 2021, pp. 392–401. doi:10.1007/978-3-030-93420-0_37. [6] M. Guillen, G. Iriarte, H. Montes, G. San Martin and N. Fantini, "Comparative Analysis of Throughput Prediction Models in SAG Mill Circuits: A Geometallurgical Approach," Mining, 5(3), 37, 2025. doi:10.3390/mining5030037. [7] Molycop, "Molycop Digital Engine: Machine Learning-accelerated SAG Mill Optimization," Research paper (industry), 25 Mar 2024. [8] P. Lopez, I. Reyes, N. Risso, M. Momayez and J. Zhang, "Machine Learning Algorithms for SemiAutogenous Grinding Mill Operational Regions' Identification," Minerals, 13(11), 1360, 2023. doi:10.3390/min13111360.
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