Hybrid modelling reduces the misspecification of expert models by combining them with machine learning (ML) components learned from data. Similarly to many ML algorithms, hybrid model performance guarantees are limited to the training distribution. Leveraging the insight that the expert model is usually valid even outside the training domain, we overcome this limitation by introducing a hybrid data augmentation strategy termed \textit{expert augmentation}. Based on a probabilistic formalization of hybrid modelling, we demonstrate that expert augmentation, which can be incorporated into existing hybrid systems, improves generalization. We empirically validate the expert augmentation on three controlled experiments modelling dynamical systems with ordinary and partial differential equations. Finally, we assess the potential real-world applicability of expert augmentation on a dataset of a real double pendulum.

翻译：混合建模通过将专家模型与从数据中学习的机器学习（ML）组件相结合，可减少专家模型的误指定问题。类似于许多机器学习算法，混合模型的性能保证仅限于训练数据分布。利用专家模型在训练域外通常仍具有有效性的洞见，我们通过引入一种称为“专家数据增强”的混合数据增强策略来克服这一局限。基于混合建模的概率形式化描述，我们证明了专家数据增强（可集成至现有混合系统中）能够提升泛化能力。我们通过三个控制实验对专家数据增强进行了实证验证，这些实验使用常微分方程与偏微分方程对动力系统进行建模。最后，我们基于真实双摆数据集评估了专家数据增强在实际场景中的潜在应用价值。