Title: Deep Learning of the Biswas-Chatterjee-Sen Model Show Chinese title

Title: 深度学习Biswas-Chatterjee-Sen模型

Abstract: We investigate the critical properties of kinetic continuous opinion dynamics using deep learning techniques. The system consists of $N$ continuous spin variables in the interval $[-1,1]$. Dense neural networks are trained on spin configuration data generated via kinetic Monte Carlo simulations, accurately identifying the critical point on both square and triangular lattices. Classical unsupervised learning with principal component analysis reproduces the magnetization and allows estimation of critical exponents. Additionally, variational autoencoders are implemented to study the phase transition through the loss function, which behaves as an order parameter. A correlation function between real and reconstructed data is defined and found to be universal at the critical point. Show Chinese abstract

Abstract: 我们使用深度学习技术研究了动力连续意见动态的临界性质。 系统由区间$[-1,1]$内的$N$个连续自旋变量组成。 密集神经网络在通过动力蒙特卡罗模拟生成的自旋配置数据上进行训练，准确地在正方形和三角形晶格上识别临界点。 使用主成分分析的经典无监督学习再现了磁化强度，并能够估计临界指数。 此外，实现了变分自编码器，通过损失函数研究相变，该函数表现得像一个序参数。 定义了真实数据和重建数据之间的相关函数，并发现该函数在临界点具有普遍性。