# Learning Coarse-Grained Dynamics on Graph

arXiv: https://arxiv.org/abs/2405.09324 · HTML: https://mlsanity.com/paper/2405.09324/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 29 references that are in the map.
- First posted on arXiv 15 May 2024.

## Builds on (most cited first, 13 of 13)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Combining Differentiable PDE Solvers and Graph Neural Networks for Fluid Flow Prediction](https://mlsanity.com/paper/2007.04439/) (2020)
- [Graph Transformation Policy Network for Chemical Reaction Prediction](https://mlsanity.com/paper/1812.09441/) (2018)
- [Data-driven parameterization of the generalized Langevin equation](https://mlsanity.com/paper/1606.02596/) (2016)
- [PIDGeuN: Graph Neural Network-Enabled Transient Dynamics Prediction of Networked Microgrids Through Full-Field Measurement](https://mlsanity.com/paper/2204.08557/) (2022)
- [Stability Conditions for Cluster Synchronization in Networks of Heterogeneous Kuramoto Oscillators](https://mlsanity.com/paper/1806.06083/) (2018)

## Abstract (arXiv)

We consider a Graph Neural Network (GNN) non-Markovian modeling framework to identify coarse-grained dynamical systems on graphs. Our main idea is to systematically determine the GNN architecture by inspecting how the leading term of the Mori-Zwanzig memory term depends on the coarse-grained interaction coefficients that encode the graph topology. Based on this analysis, we found that the appropriate GNN architecture that will account for K-hop dynamical interactions has to employ a Message Passing (MP) mechanism with at least 2K steps. We also deduce that the memory length required for an accurate closure model decreases as a function of the interaction strength under the assumption that the interaction strength exhibits a power law that decays as a function of the hop distance. Supporting numerical demonstrations on two examples, a heterogeneous Kuramoto oscillator model and a power system, suggest that the proposed GNN architecture can predict the coarse-grained dynamics under fixed and time-varying graph topologies.