Hybrid modeling, the combination of machine learning models and scientific mathematical models, enables flexible and robust data-driven prediction with partial interpretability. However, effectively the scientific models may be ignored in prediction due to the flexibility of the machine learning model, making the idea of hybrid modeling pointless. Typically some regularization is applied to hybrid model learning to avoid such a failure case, but the formulation of the regularizer strongly depends on model architectures and domain knowledge. In this paper, we propose to focus on the flatness of loss minima in learning hybrid models, aiming to make the model as simple as possible. We employ the idea of sharpness-aware minimization and adapt it to the hybrid modeling setting. Numerical experiments show that the SAM-based method works well across different choices of models and datasets.

翻译：混合建模，即机器学习模型与科学数学模型的结合，能够实现兼具部分可解释性的灵活且鲁棒的数据驱动预测。然而，由于机器学习模型的灵活性，科学模型在预测中可能被有效忽略，从而使混合建模的理念失去意义。通常，在混合模型学习中会应用某种正则化来避免此类失败情况，但正则化器的形式在很大程度上依赖于模型架构和领域知识。在本文中，我们提出关注混合模型学习中损失最小值的平坦性，旨在使模型尽可能简单。我们采用锐度感知最小化的思想，并将其适配到混合建模场景中。数值实验表明，基于SAM的方法在不同模型选择和数据集上均表现良好。