| Abstract | Mining activities generate substantial amounts of waste rock, which are often disposed of in waste rock piles. Drainage from these piles can pose serious environmental risks. It is crucial to reliably predict drainage properties in order to effectively manage them. In previous work, we developed a machine learning model to predict waste rock drainage quantity using weather monitoring data as the input and drainage flow rate as the output. However, this model lacked physical constraints, limiting its interpretability, reliability, and applicability. In this study, we introduced a new machine learning model designed with physical constraints to improve the predictions of drainage quantity. This new model incorporates a weather refining sub-model and integrates physical constraints to enhance the overall reliability of the model predictions. The weather refining sub-model transforms primary weather features (total precipitation and temperature) into secondary features (rainfall, snowmelt, and evaporation) through established mathematical relationships. These secondary features were then used as inputs for the machine learning model to predict drainage quantity. To embed physical principles within the machine learning model, we integrated a water balance equation into the neural network architecture and modified the loss function accordingly. In addition, we included an adjustable bias term to optimize the balance between model performance and interpretability. Compared with our previous model, the incorporation of physical constraints into the machine learning model improved the accuracy of the drainage quantity predictions. More importantly, this approach ensures that the model outputs adhere to physical laws, thereby enhancing its interpretability, reliability, and applicability. |
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