Deep learning assisted physics-based modeling of aluminum extraction process

Modeling complex physical processes such as the extraction of aluminum is mainly done using pure physics-based models derived from first principles. However, the accuracy of these models can often suffer due to a partial understanding of the process, uncertainty in the input parameters, and numerous modeling assumptions. More recently, with the ever-increasing availability of data, there has been an explosion of interest in applying modern machine learning methods because of their ability to learn complex mappings directly from data. Unfortunately, these models tend to be black boxes, require an enormous amount of data, and do not utilize existing domain knowledge. In this work, we develop a novel approach combining physics-based and data-driven modeling approaches while eliminating some weaknesses. We use a data-driven model to correct a misspecified physics-based model of the Hall–Héroult process in an aluminum electrolysis cell using a corrective source term added to the set of governing ordinary differential equations. Our approach ensures that the existing knowledge is utilized to the maximum extent possible while relying on the data-driven models only to model those aspects which the physics-based model does not represent well. We compare this approach with an end-to-end learning approach and an ablated physics-based model, showing that the proposed hybrid method is more accurate, consistent, and stable for long-term predictions.