# Learning dynamical systems with biochemically informed neural ordinary differential equations

arXiv: https://arxiv.org/abs/2605.24170 · HTML: https://mlsanity.com/paper/2605.24170/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 66 references that are in the map.
- First posted on arXiv 22 May 2026.

## Builds on (most cited first, 12 of 12)

- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [The Expressive Power of Neural Networks: A View from the Width](https://mlsanity.com/paper/1709.02540/) (2017)
- [Benefits of depth in neural networks](https://mlsanity.com/paper/1602.04485/) (2016)
- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [Learning effective stochastic differential equations from microscopic simulations: linking stochastic numerics to deep learning](https://mlsanity.com/paper/2106.09004/) (2021)
- [AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification](https://mlsanity.com/paper/2310.01433/) (2023)
- [Interpretable Polynomial Neural Ordinary Differential Equations](https://mlsanity.com/paper/2208.05072/) (2022)
- [Learning Dynamical Systems with Side Information](https://mlsanity.com/paper/2008.10135/) (2020)
- [Why ReLU Units Sometimes Die: Analysis of Single-Unit Error Backpropagation in Neural Networks](https://mlsanity.com/paper/1812.05981/) (2018)
- [Surrogate Modeling and Control of Medical Digital Twins](https://mlsanity.com/paper/2402.05750/) (2024)
- [Control of Medical Digital Twins with Artificial Neural Networks](https://mlsanity.com/paper/2403.13851/) (2024)

## Built on by (most cited first, 1 of 1)

- [Neural Petri flows for chemical reactions](https://mlsanity.com/paper/2610.08750/) (2026)

## Abstract (arXiv)

Ordinary differential equation models of biochemical reactions are often formulated as stoichiometric systems in which the dynamics arise from a collection of interacting processes. A central challenge is that the functional form of each process is rarely known a priori and may be difficult to infer from data. We propose biochemically informed neural ordinary differential equations (BINODEs), a neural-ODE framework that retains the stoichiometric structure of mechanistic models while representing individual processes by neural networks. In BINODEs, the outputs of neural network processes (NNPs) are mapped to state derivatives through a linear layer analogous to a stoichiometric matrix. This architecture allows biological side information, such as process-specific inputs, sign constraints, and monotonicity assumptions, to be built directly into the model. We characterize the approximation properties of NNPs for several standard biochemical rate laws and show that the proposed framework recovers both trajectories and process-level structure in Monod, Lotka--Volterra, pharmacokinetic, and ultradian endocrine models. These results suggest that BINODEs offer a useful compromise between mechanistic interpretability and data-driven flexibility for modeling partially known biochemical or biological dynamical systems.