标题： 三临界点的三临界定向渗流是基于神经网络确定的 显示英文标题

标题： The tricritical point of tricritical directed percolation is determined based on neural network

摘要： 近年来，神经网络被越来越多地用于识别相变的关键点。 对于三临界定向渗透模型，其稳态构型包括一阶和二阶相变。 由于存在交叉效应，识别相变的关键点变得具有挑战性。 本研究利用蒙特卡洛模拟在不同概率 $p$ 和 $q$ 下获得稳态构型，并通过计算平均粒子密度的增量，我们观察到一阶相变、二阶相变以及两种类型相变相互作用的区域。这些蒙特卡洛生成的稳态构型被用作输入来构建和训练卷积神经网络，从而确定不同概率 $q$ 的关键点 $p_{c}$。 此外，通过学习与过热点 $p=p_u$相关的稳态构型，我们将三临界点定位在 $q_{t}=0.893$。 同时，我们采用了一个三输出的CNN模型来获得相变边界和交叉区域的范围。 我们的方法提供了一种基于神经网络的方法来捕捉关键点并区分相变边界，为这一问题提供了一个新的解决方案。 显示英文摘要

摘要： In recent years, neural networks have increasingly been employed to identify critical points of phase transitions. For the tricritical directed percolation model, its steady-state configurations encompass both first-order and second-order phase transitions. Due to the presence of crossover effects, identifying the critical points of phase transitions becomes challenging. This study utilizes Monte Carlo simulations to obtain steady-state configurations under different probabilities $p$ and $q$, and by calculating the increments in average particle density, we observe first-order transitions, second-order transitions, and regions where both types of transitions interact.These Monte Carlo-generated steady-state configurations are used as input to construct and train a convolutional neural network, from which we determine the critical points $p_{c}$ for different probabilities $q$. Furthermore, by learning the steady-state configurations associated with the superheated point $p=p_u$, we locate the tricritical point at $q_{t}=0.893$. Simultaneously, we employed a three-output CNN model to obtain the phase transition boundaries and the range of the crossover regions. Our method offers a neural network-based approach to capture critical points and distinguish phase transition boundaries, providing a novel solution to this problem.