Non-Negative Universal Differential Equations With Applications in Systems Biology
This work addresses a specific problem in systems biology modeling by ensuring realistic solutions in hybrid mechanistic-neural network models, representing an incremental improvement.
The paper tackled the issue of unrealistic negative values in universal differential equations (UDEs) when modeling biochemical systems by introducing non-negative UDEs (nUDEs) that guarantee non-negative solutions, and they explored regularization techniques to enhance generalization and interpretability.
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.