Machine learning phases in swarming systems

Abstract

Recent years have witnessed a growing interest in using machine learning to predict and identify phase transitions in various systems. Here we adopt convolutional neural networks (CNNs) to study the phase transitions of Vicsek model, solving the problem that traditional order parameters are insufficiently able to do. Within the large-scale simulations, there are four phases, and we confirm that all the phase transitions between two neighboring phases are first-order. We have successfully classified the phase by using CNNs with a high accuracy and identified the phase transition points, while traditional approaches using various order parameters fail to obtain. These results indicate the great potential of machine learning approach in understanding the complexities in collective behaviors, and in related complex systems in general.

Consequence of anisotropy on flocking: the discretized Vicsek model

“…Interestingly, in the intermediate noise amplitudes (∼ η = 0.28−0.35), the system exhibits bistability where both cross-sea and microphase features can be found depending upon the initial conditions. In the VM, bistability was observed between the ordered phase and cross-sea phase and also between the microphase and disordered phase [35]. This bistability arises due to the fluctuation at relatively higher noise amplitudes and finite system size.…”

“…This is a consequence of having more particle orientations allowed through q. The cross-sea phase, where interactions become more intense due to the characteristics of the band structure, appears between the polar liquid phase and the parallel band state [35] for a fixed q. This phase is not simply a superposition of waves of inclined bands, but an independent self-organized complex pattern with an inherently selected crossing angle.…”

“…The polar order parameter m is also insensitive around the cross-sea state. Thus, for precise quantification of different phases and their boundaries, we compute the structural order parameter C 2 [26,35,36] as follows:…”

Machine learning methods for liquid crystal research: phases, textures, defects and physical properties

“…Different ML approaches such as artificial neural network (ANN), convolutional neural network (CNN), reinforcement learning, deep learning techniques and others are widely used for molecular property prediction and chemical discovery, multiscale simulation and analysis, 7 structural formation analysis based on image recognition, 11 inverse design of colloidal interactions to stabilize the desired structure, 12 controlling collective behavior in non-equilibrium systems, 13 characterization of topological phases of matter in lattice systems, the prediction of phase transitions in off-lattice and atomistic simulations, 14 prediction of phase separations 15 and transitions. 16 When applied to liquid crystal materials, these methods hold the promise of accelerating the discovery and optimization of new materials, as well as providing a deeper insight into the fundamental principles governing their behavior.…”

Laplacian dynamics of convergent and divergent collective behaviors

“…It is unclear whether the convergent and divergent dynamics of organic evolution, the convergent and divergent social behaviors of people, and any other similar phenomenon can be characterized by a unified and simple model. While specialized models [1,2,[17][18][19][20][21][22][23][24], statistical analyses [25][26][27][28][29], and data-driven methods [30][31][32][33] have achieved essential progress in studying collective dynamics, advances in describing the convergent and divergent evolution processes of collective behaviors remain limited.…”