Current state and open problems in universal differential equations for systems biology.

Universal Differential Equations (UDEs) combine mechanistic differential equations with data-driven artificial neural networks, forming a flexible framework for modelling complex biological systems. This hybrid approach leverages prior knowledge and data to uncover unknown processes and deliver accurate predictions. However, UDEs face challenges in efficient and reliable training due to stiff dynamics and noisy, sparse data common in biology, and in ensuring the interpretability of the parameters of the mechanistic model. We investigate these challenges and evaluate UDE performance on realistic biological scenarios, providing a systematic training pipeline. Our results demonstrate the versatility of UDEs in systems biology and reveal that noise and limited data significantly degrade performance, but regularisation can improve accuracy and interpretability. By addressing key challenges and offering practical solutions, this work advances UDE methodology and underscores its potential in tackling complex problems in systems biology.