# Learning Dynamics and Structure of Complex Systems Using Graph Neural Networks

arXiv: https://arxiv.org/abs/2202.10996 · HTML: https://mlsanity.com/paper/2202.10996/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 24 references that are in the map.
- First posted on arXiv 22 Feb 2022.

## Builds on (most cited first, 18 of 18)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Neural Relational Inference for Interacting Systems](https://mlsanity.com/paper/1802.04687/) (2018)
- [Efficient Graph Generation with Graph Recurrent Attention Networks](https://mlsanity.com/paper/1910.00760/) (2019)
- [A Compositional Object-Based Approach to Learning Physical Dynamics](https://mlsanity.com/paper/1612.00341/) (2016)
- [Visual Interaction Networks](https://mlsanity.com/paper/1706.01433/) (2017)
- [GMNN: Graph Markov Neural Networks](https://mlsanity.com/paper/1905.06214/) (2019)
- [Loopy Belief Propagation for Approximate Inference: An Empirical Study](https://mlsanity.com/paper/1301.6725/) (2013)
- [Inference in Probabilistic Graphical Models by Graph Neural Networks](https://mlsanity.com/paper/1803.07710/) (2018)
- [Combining Generative and Discriminative Models for Hybrid Inference](https://mlsanity.com/paper/1906.02547/) (2019)
- [Factor Graph Neural Network](https://mlsanity.com/paper/1906.00554/) (2019)

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

- [Learning Heterogeneous Interaction Strengths by Trajectory Prediction with Graph Neural Network](https://mlsanity.com/paper/2208.13179/) (2022)
- [Inferring Inference](https://mlsanity.com/paper/2310.03186/) (2023)

## Abstract (arXiv)

Many complex systems are composed of interacting parts, and the underlying laws are usually simple and universal. While graph neural networks provide a useful relational inductive bias for modeling such systems, generalization to new system instances of the same type is less studied. In this work we trained graph neural networks to fit time series from an example nonlinear dynamical system, the belief propagation algorithm. We found simple interpretations of the learned representation and model components, and they are consistent with core properties of the probabilistic inference algorithm. We successfully identified a 'graph translator' between the statistical interactions in belief propagation and parameters of the corresponding trained network, and showed that it enables two types of novel generalization: to recover the underlying structure of a new system instance based solely on time series observations, or to construct a new network from this structure directly. Our results demonstrated a path towards understanding both dynamics and structure of a complex system and how such understanding can be used for generalization.