Methodologically, the explicit representation → dynamics split is key in a noisy, nonstationary industrial environment: the CVAE learns a compact and robust latent state from multivariate observation windows of the primary grinding line, and the MDN-RNN models the evolution of that state conditioned on actions and exogenous inputs. This enables not only point forecasts but also state-dependent uncertainty (P10–P90 bands), which typically widens during regime transitions (e.g., changes in ore characteristics or feed conditions) and narrows during steadier periods, providing risk-aware information for decision-making. Performance varies by signal type. Variables that are more directly coupled to actions/setpoints and exhibit smoother minute-scale dynamics tend to yield lower errors (e.g., throughput, pressures, power, 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.
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