Spatial distribution order parameter prediction of collective system using graph network

Abstract

In the past few decades, the study of collective motion phase transition process has made great progress. It is also important for the description of the spatial distribution of particles. In this work, we propose a new order parameter $\varphi$ to quantify the degree of order in the spatial distribution of particles. The results show that the spatial distribution order parameter can effectively describe the transition from a disorderly moving phase to a phase with a coherent motion of the particle distribution and the same conclusion could be obtained for systems with different sizes. Furthermore, we develop a powerful Molecular Dynamic Graph Network(MDGNet) model to realize the long-term prediction of the self-propelled collective system solely from the initial particle positions and movement angles. Employing this model, we successfully predict the order parameters of the specified time step. And the model can also be applied to analyze other types of complex system with local interactions.

Physical information-enhanced graph neural network for predicting phase separation

“…This approach allows us to analyze the spatial distribution of particles and their evolution. The order parameter ϕ is defined as follows: [33] ϕ =…”

“…[20][21][22][23][24][25] Since the past decade, machine learning has been used to solve classic problems in complex physical systems. [26][27][28][29][30][31][32][33][34] In particular, the graph network-based simulators show extraordinary predictive capabilities for physical systems such as fluids and rigid solids, thanks to the ability of graph networks to effectively capture relational information and structural properties in the system. [35] At the same time, researchers have successfully used the features of GNNs to predict the longterm dynamics of glass systems.…”

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