# Neural Ordinary Differential Equations for Simulating Metabolic Pathway Dynamics from Time-Series Multiomics Data

arXiv: https://arxiv.org/abs/2512.08732 · HTML: https://mlsanity.com/paper/2512.08732/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 9 Dec 2025.

## Builds on (most cited first, 7 of 7)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [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)
- [Depth-Width Tradeoffs in Approximating Natural Functions with Neural Networks](https://mlsanity.com/paper/1610.09887/) (2016)
- [Learning Specialized Activation Functions for Physics-informed Neural Networks](https://mlsanity.com/paper/2308.04073/) (2023)
- [A Robust SINDy Approach by Combining Neural Networks and an Integral Form](https://mlsanity.com/paper/2309.07193/) (2023)

## Abstract (arXiv)

The advancement of human healthspan and bioengineering relies heavily on predicting the behavior of complex biological systems. While high-throughput multiomics data is becoming increasingly abundant, converting this data into actionable predictive models remains a bottleneck. High-capacity, datadriven simulation systems are critical in this landscape; unlike classical mechanistic models restricted by prior knowledge, these architectures can infer latent interactions directly from observational data, allowing for the simulation of temporal trajectories and the anticipation of downstream intervention effects in personalized medicine and synthetic biology. To address this challenge, we introduce Neural Ordinary Differential Equations (NODEs) as a dynamic framework for learning the complex interplay between the proteome and metabolome. We applied this framework to time-series data derived from engineered Escherichia coli strains, modeling the continuous dynamics of metabolic pathways. The proposed NODE architecture demonstrates superior performance in capturing system dynamics compared to traditional machine learning pipelines. Our results show a greater than 90% improvement in root mean squared error over baselines across both Limonene (up to 94.38% improvement) and Isopentenol (up to 97.65% improvement) pathway datasets. Furthermore, the NODE models demonstrated a 1000x acceleration in inference time, establishing them as a scalable, high-fidelity tool for the next generation of metabolic engineering and biological discovery.