Non-Negative Universal Differential Equations With Applications in Systems Biology

TL;DR

This paper introduces non-negative universal differential equations (nUDEs) that ensure biochemical quantities remain non-negative, addressing a key limitation of traditional UDEs, and explores regularisation techniques to enhance model generalisation and interpretability.

Contribution

The paper proposes a novel non-negative constrained UDE framework and investigates regularisation methods to improve model robustness and interpretability in systems biology.

Findings

nUDEs guarantee non-negativity of solutions

Regularisation improves model generalisation

Enhanced interpretability of hybrid models

Abstract

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.