Estimation of Particle Location in Granular Materials Based on Graph Neural Networks

Abstract

Particle locations determine the whole structure of a granular system, which is crucial to understanding various anomalous behaviors in glasses and amorphous solids. How to accurately determine the coordinates of each particle in such materials within a short time has always been a challenge. In this paper, we use an improved graph convolutional neural network to estimate the particle locations in two-dimensional photoelastic granular materials purely from the knowledge of the distances for each particle, which can be estimated in advance via a distance estimation algorithm. The robustness and effectiveness of our model are verified by testing other granular systems with different disorder degrees, as well as systems with different configurations. In this study, we attempt to provide a new route to the structural information of granular systems irrelevant to dimensionality, compositions, or other material properties.

Keywords: coordinate prediction; distance estimation algorithm; distance information; graph convolutional network; particle locations; two-dimensional photoelastic granular materials.

Figure A1

Granular system coordinate diagram and coordinate prediction diagram. (a₁–h₁) Coordinate diagram of granular system with eight different configurations (conf1, conf2, conf4–conf7, conf9, and conf10). (a₂–h₂) Coordinate prediction diagram corresponding to (a₁–h₁), respectively. The RMSE values are 0.0328, 0.0332, 0.0330, 0.0343, 0.0340, 0.0331, 0.0384, and 0.0355, corresponding to (a₁–h₁), respectively.

Figure 1

Construction of graph network. (Left) Partial particles of a particle system with a disorder of 1 to 1. (Right) Graph network constructed by one-hop neighbors of particles in left.

Figure 2

Distance estimation methods. (a) graph network; (b) minimum hop path algorithm; (c) shortest path algorithm.

Figure 3

The principle of the 2-layer GCN. Diagram of GCN updating rule for hidden layer in the virtual box.

Figure 4

Root-mean-squared error (RMSE) versus hop counts (H). The number of anchor nodes in all systems is about 60% of the total number of nodes.

Figure 5

Effective prediction accuracy (EPA) versus hop counts (H). The number of anchor nodes in all systems is about 60% of the total number of nodes.

Figure 6

Granular system coordinate diagram, coordinate prediction diagram, and comparison diagram. The red particle map is the original coordinate map of the granular system, the blue particle map is the prediction map, the magenta particles are the effective prediction particles, and the orange particles are the ineffective prediction particles. Moreover, (a–c) show the 1:0 granular system where the RMSE is 0.0302 and the EPA is 95.78%; (d–f) show the 1:1 granular system where the RMSE is 0.0357 and the EPA is 93.1%; and (g–i) show the 2.16:1 granular system where the RMSE is 0.0417 and the EPA is 85.6%.

Figure 7

The prediction results for granular systems with different configurations of the disorder degree of 1:1. (Left) Root-mean-squared error (RMSE) versus configuration. (Right) Effective prediction accuracy (EPA) versus configuration.

Figure 8

The prediction results for granular systems with different configurations of the disorder degree of 1:1. The red particle map is the original coordinate map of the granular system, the blue particle map is the prediction map, the magenta particles are the effective prediction particles, and the orange particles are the ineffective prediction particles. Moreover, (a–c) show a granular system of conf2 where the RMSE is 0.0375 and the EPA is 91.79%; (d–f) show a granular system of conf4 where the RMSE is 0.0350 and the EPA is 93.05%.

Figure 9

Root-mean-squared error (RMSE) versus configurations.

Figure 10

Granular system coordinate diagram and coordinate prediction diagram. (a,b) are the granular system coordinate diagram and the coordinate prediction diagram of conf3. The RMSE of conf3 is 0.0319. (c,d) are the granular system coordinate diagram and the coordinate prediction diagram of conf8. The RMSE of conf8 is 0.0325.