# Graph Element Networks: adaptive, structured computation and memory

@article{Alet2019GraphEN, title={Graph Element Networks: adaptive, structured computation and memory}, author={Ferran Alet and Adarsh K. Jeewajee and Maria Bauz{\'a} and Alberto Rodriguez and Tomas Lozano-Perez and Leslie Pack Kaelbling}, journal={ArXiv}, year={2019}, volume={abs/1904.09019} }

We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. [... ] Key Method We use GNNs as a computational substrate, and show that the locations of the nodes in space as well as their connectivity can be optimized to focus on the most complex parts of the space. Moreover, this representational strategy allows the learned input-output relationship to generalize over the size of the underlying space and run the same model at different levels… Expand

## 35 Citations

### Learning Connectivity with Graph Convolutional Networks

- Computer Science2020 25th International Conference on Pattern Recognition (ICPR)
- 2021

Experiments conducted on the challenging task of skeleton-based action recognition shows the superiority of the proposed framework for graph convolutional networks that learns the topological properties of graphs compared to handcrafted graph design as well as the related work.

### Neural Operator: Graph Kernel Network for Partial Differential Equations

- Computer Science, MathematicsICLR 2020
- 2020

The key innovation in this work is that a single set of network parameters, within a carefully designed network architecture, may be used to describe mappings between infinite-dimensional spaces and between different finite-dimensional approximations of those spaces.

### Simulating Continuum Mechanics with Multi-Scale Graph Neural Networks

- Computer ScienceArXiv
- 2021

The proposed MultiScaleGNN model is a novel multi-scale graph neural network model for learning to infer unsteady continuum mechanics that can generalise from uniform advection fields to high-gradient fields on complex domains at test time and infer long-term Navier-Stokes solutions within a range of Reynolds numbers.

### EQUIVARIANT GRAPH CONVOLUTIONAL NETWORKS

- Computer Science
- 2021

This paper proposes a set of transformation invariant and equivariant models based on graph convolutional networks, called IsoGCNs, and demonstrates that the proposed model has a competitive performance compared to state-of-the-art methods on tasks related to geometrical and physical simulation data.

### Learning the Solution Operator of Boundary Value Problems using Graph Neural Networks

- Computer Science
- 2022

GNNs can be used to learn solution operators that generalize over a range of properties and produce solutions much faster than a generic solver, and this work designs a general solution operator for two different time-independent PDEs using graph neural networks and spectral graph convolutions.

### Physics-Embedded Neural Networks: $\boldsymbol{\mathrm{E}(n)}$-Equivariant Graph Neural PDE Solvers

- Computer Science
- 2022

This work presents an approach termed physics-embedded neural networks that considers boundary conditions and predicts the state after a long time using an implicit method, and demonstrates that the model learns phenomena in complex shapes and outperforms a well-optimized classical solver and a state-of-the-art machine learning model in speed-accuracy trade-off.

### Convergent Graph Solvers

- Computer Science, MathematicsICLR
- 2022

We propose the convergent graph solver (CGS)1, a deep learning method that learns iterative mappings to predict the properties of a graph system at its stationary state (fixed point) with guaranteed…

### Learning Connectivity with Graph Convolutional Networks for Skeleton-based Action Recognition

- Computer ScienceArXiv
- 2021

Experiments conducted on the challenging task of skeleton-based action recognition shows the superiority of the proposed framework for graph convolutional networks that learns the topological properties of graphs compared to handcrafted graph design as well as the related work.

### Learning Mesh-Based Simulation with Graph Networks

- Computer ScienceICLR
- 2021

MeshGraphNets is introduced, a framework for learning mesh-based simulations using graph neural networks that can be trained to pass messages on a mesh graph and to adapt the mesh discretization during forward simulation, and can accurately predict the dynamics of a wide range of physical systems.

### Deep learning of material transport in complex neurite networks

- Materials Science, Computer ScienceScientific reports
- 2021

A graph neural network (GNN)-based deep learning model is presented to learn the IGA-based material transport simulation and provide fast material concentration prediction within neurite networks of any topology.

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