Universal differential equations (UDEs) leverage the respective advantages of mechanistic models and artificial neural networks and combine them into one dynamic model. However, these hybrid models can suffer from unrealistic solutions, such as negative values for biochemical quantities. We present non-negative UDE (nUDEs), a constrained UDE variant that guarantees non-negative values. Furthermore, we explore regularisation techniques to improve generalisation and interpretability of UDEs.

翻译：通用微分方程（UDEs）结合了机理模型与人工神经网络各自的优势，将其融合为一个动态模型。然而，这类混合模型可能产生不现实的解，例如生化量出现负值。本文提出非负通用微分方程（nUDEs），这是一种能保证非负值的约束型通用微分方程变体。此外，我们探索了正则化技术以提升通用微分方程的可泛化性与可解释性。