# Structural Inference of Networked Dynamical Systems with Universal Differential Equations

arXiv: https://arxiv.org/abs/2207.04962 · HTML: https://mlsanity.com/paper/2207.04962/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 40 references that are in the map.
- First posted on arXiv 11 Jul 2022.

## Builds on (most cited first, 16 of 16)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Graph-Coupled Oscillator Networks](https://mlsanity.com/paper/2202.02296/) (2022)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [PDE-GCN: Novel Architectures for Graph Neural Networks Motivated by Partial Differential Equations](https://mlsanity.com/paper/2108.01938/) (2021)
- [Autonomous Discovery of Unknown Reaction Pathways from Data by Chemical Reaction Neural Network](https://mlsanity.com/paper/2002.09062/) (2020)
- [ChemNODE: A Neural Ordinary Differential Equations Approach for Chemical Kinetics Solvers](https://mlsanity.com/paper/2101.04749/) (2020)
- [Neural Ordinary Differential Equation Control of Dynamics on Graphs](https://mlsanity.com/paper/2006.09773/) (2020)
- [A General Deep Learning Framework for Network Reconstruction and Dynamics Learning](https://mlsanity.com/paper/1812.11482/) (2018)
- [Constrained Block Nonlinear Neural Dynamical Models](https://mlsanity.com/paper/2101.01864/) (2021)
- [Robust Reconstruction of Complex Networks from Sparse Data](https://mlsanity.com/paper/1501.04731/) (2015)

## Built on by (most cited first, 2 of 2)

- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Learning Neural Differential Algebraic Equations via Operator Splitting](https://mlsanity.com/paper/2403.12938/) (2024)

## Abstract (arXiv)

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical) units to exhibit a wide range of nontrivial behaviors, such as the emergence of coherent structures (e.g., waves and patterns) or otherwise notable dynamics (e.g., synchrony and chaos). In this work, we seek to infer (i) the intrinsic physics of a base unit of a population, (ii) the underlying graphical structure shared between units, and (iii) the coupling physics of a given networked dynamical system given observations of nodal states. These tasks are formulated around the notion of the Universal Differential Equation, whereby unknown dynamical systems can be approximated with neural networks, mathematical terms known a priori (albeit with unknown parameterizations), or combinations of the two. We demonstrate the value of these inference tasks by investigating not only future state predictions but also the inference of system behavior on varied network topologies. The effectiveness and utility of these methods is shown with their application to canonical networked nonlinear coupled oscillators.