# Non-Negative Universal Differential Equations With Applications in Systems Biology

arXiv: https://arxiv.org/abs/2406.14246 · HTML: https://mlsanity.com/paper/2406.14246/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 19 references that are in the map.
- First posted on arXiv 20 Jun 2024.

## Builds on (most cited first, 3 of 3)

- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)

## Built on by (most cited first, 5 of 5)

- [Developing hybrid mechanistic and data-driven personalized prediction models for platelet dynamics](https://mlsanity.com/paper/2505.21204/) (2025)
- [Bayesian Symbolic Regression for Missing Physics](https://mlsanity.com/paper/2603.14918/) (2026)
- [Experimental Design for Missing Physics](https://mlsanity.com/paper/2604.01231/) (2026)
- [Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming](https://mlsanity.com/paper/2606.06094/) (2026)
- [Hyperparameter selection for equation learning with biologically-informed neural networks](https://mlsanity.com/paper/2610.02954/) (2026)

## Abstract (arXiv)

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.