核物质物态方程的物理可容许性的深度学习分类
Deep-learning classification of physically admissible nuclear-matter equations of state
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中文总结 AI 辅助
本研究开发仅基于归一化压强曲面的卷积神经网络，快速且框架无关地分类核物质物态方程的物理可容许性，在测试数据上准确率达97.65%，速度约为直接验证的20倍。
中文摘要 AI 辅助
热力学稳定性与因果性对核物质的物态方程（EoS）施加了基本约束。传统上验证这些约束需要计算比热、重子数 susceptibility、声速等物理量，当需要检验大量候选EoS时，计算开销会变得很高。本研究探究归一化压强曲面 $Q(T,\mu_B)=P(T,\mu_B)/T^4$ 是否单独包含足够信息来确定EoS的物理可容许性。我们开发了一种监督式卷积神经网络（CNN），仅使用该压强表示将EoS分类为物理可容许或不可容许。网络的训练标签来自直接的热力学稳定性与因果性检验，且未获取底层EoS框架的任何参数信息。对于在伊辛映射（Ising-mapping）框架内生成的EoS，该模型在未见的测试数据上达到97.65%的准确率；独立应用于来自不同全息（holographic）框架的EoS时，它对测试集实现了完美分类。这些结果表明，压强曲面包含可被CNN直接学习的热力学稳定性与因果性违反的几何特征。由于分类器仅依赖压强曲面，其在推理过程中无需评估高阶热力学可观测量，且在很大程度上独立于EoS生成框架。当压强曲面以二维数组形式提供时，机器学习验证的速度约为直接验证的20倍。本研究的结果确立了一种快速、框架无关的方法，可直接从压强曲面识别物理可容许的EoS。
英文摘要
Thermodynamic stability and causality impose fundamental constraints on the equation of state (EoS) of nuclear matter. Verifying these constraints conventionally requires calculating quantities such as the specific heat, baryon-number susceptibility, and speed of sound, which can become computationally expensive when many candidate EoSs must be examined. We investigate whether the normalized pressure surface, $Q(T,μ_B)=P(T,μ_B)/T^4$, alone contains sufficient information to determine the physical admissibility of an EoS. We develop a supervised convolutional neural network (CNN) that uses only this pressure representation to classify EoSs as physically admissible or inadmissible. The network is provided with training labels obtained from direct thermodynmaic stability and causality check and its does not get any information about the parameters of the underlying EoS framework. For EoSs generated within an Ising-mapping framework, the model achieves $97.65%$ accuracy on unseen test data. Applied independently to EoSs from a distinct holographic framework, it achieves perfect classification of the test set. These results show that pressure surfaces contain geometric signatures of thermodynamic stability and causality violations that can be learned directly by a CNN. Because the classifier relies only on the pressure surface, it avoids evaluating higher-order thermodynamic observables during inference and is largely independent of the EoS-generation framework. When the pressure surface is supplied as a two-dimensional array, the machine-learning validation is approximately 20 times faster than direct validation. Our results establish a fast, framework-independent approach for identifying physically admissible EoSs directly from their pressure surfaces.
