## 4 Related Work  
This section reviews key research on control strategies and overload detection methods to address the challenges of overload forecasting in semi-autogenous grinding (SAG) mills. It begins by examining classification techniques for different types of overloads, followed by a discussion on approaches to identifying overload conditions. The role of simulations and advanced algorithms in optimizing mill operations is also explored. Additionally, the section highlights the application of Gram matrices to enhance predictive models. It reviews recent advancements in physics-informed neural networks (PINNs), emphasizing their potential to integrate physical laws with machine learning for improved overload prediction accuracy. This review outlines the progress and remaining challenges in the field, providing a foundation for the proposed methodologies in subsequent sections. Optimizing grinding processes is essential in mineral processing, as milling operations significantly influence plant efficiency and account for 50-70% of operational costs. Machine learning (ML) and advanced control strategies offer promising solutions for the complex challenges of semi-autogenous (SAG) mill operations. [PERSON] et al. [9] introduced a model predictive control (MPC) approach designed explicitly for SAG mills, leveraging a detailed process model to optimize performance under varying conditions. This approach addressed the limitations of traditional PID controllers, which struggled with the multivariable interactions and nonlinear dynamics of grinding processes. Focusing on critical variables such as drawing power, volumetric filling level, and size reduction while manipulating parameters like ore feed rate, water feed rate, and mill rotation speed, the MPC strategy demonstrated robust performance by mitigating noise disturbances and fluctuating conditions. This innovation marks a significant step toward harnessing ML and control theory to improve the efficiency and predictability of SAG milling operations, a cornerstone of the mineral processing industry. [PERSON] et al. [21] highlighted the importance of optimizing grinding processes in ball mills to improve energy efficiency, noting that only a tiny portion of the energy consumed contributes to particle size reduction. The study explored control strategies to enhance grinding circuit efficiency without altering the final product size. Model-based predictive control (MPC) was compared with conventional systems, demonstrating that MPC could increase throughput and reduce specific energy consumption by effectively managing product size distribution, preventing overgrinding, and optimizing mill performance. Additionally, MPC adapted to changes in feed properties, maintaining superior energy efficiency under varying operational conditions. [PERSON] et al. [22] developed a real-time optimization (RTO) system leveraging genetic algorithms (GAs) to improve the performance of semi-autogenous grinding (SAG) mills. This system optimized key operational parameters to maximize ore throughput and grinding efficiency while respecting constraints such as maximum ore feed rate and mill power draw. The study showed that the GA-based RTO system significantly enhanced mill performance, achieving up to a 50% improvement in performance indices compared to baseline conditions. This method provides a robust alternative to traditional optimization techniques, which often need help with milling processes' complex, nonlinear nature. [PERSON] et al. [17] explored the discrete element method (DEM) for optimizing mill rotation speed, providing valuable insights into integrating machine learning (ML) techniques for predictive maintenance and overload detection in SAG mills. The study emphasized the importance of accurate, real-time data analysis for operational adjustments, demonstrating how precise control over mill speed, informed by particle movement and grinding efficiency, significantly improves mill performance.