With the ever-increasing availability of data, there has been an explosion of interest in applying modern machine learning methods to fields such as modeling and control. However, despite the flexibility and surprising accuracy of such black-box models, it remains difficult to trust them. Recent efforts to combine the two approaches aim to develop flexible models that nonetheless generalize well; a paradigm we call Hybrid Analysis and modeling (HAM). In this work we investigate the Corrective Source Term Approach (CoSTA), which uses a data-driven model to correct a misspecified physics-based model. This enables us to develop models that make accurate predictions even when the underlying physics of the problem is not well understood. We apply CoSTA to model the Hall-H\'eroult process in an aluminum electrolysis cell. We demonstrate that the method improves both accuracy and predictive stability, yielding an overall more trustworthy model.

翻译：随着数据日益丰富，现代机器学习方法在建模与控制等领域的应用引起了广泛关注。然而，尽管此类黑箱模型具有灵活性和惊人的准确性，但其可信度仍难以保证。近期将两种方法结合的努力旨在开发兼具灵活性与泛化能力的模型——我们称之为混合分析与建模（Hybrid Analysis and Modeling, HAM）。本研究探讨了修正源项方法（Corrective Source Term Approach, CoSTA），该方法利用数据驱动模型修正指定错误的物理模型。这使得我们能够在问题潜在物理机制尚不完全明确的情况下，构建出能够做出准确预测的模型。我们将CoSTA应用于铝电解槽中霍尔-埃鲁特过程的建模。结果表明，该方法同时提升了模型的准确性和预测稳定性，最终构建出整体更为可信的模型。