组等价自编码器用于识别自发破碎的对称性
Devanshu Agrawal1, Adrian Del Maestro2,3,4, Steven Johnston2,4
1Department of Industrial and Systems Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA.
Physical review. E
|June 17, 2023
概括
我们开发了一种群体等价自编码器 (GE自编码器),通过检测物理系统中的破碎对称性来识别相位边界. 这种深度学习方法准确地确定了临界温度和相位过渡,提高了效率.
科学领域:
- 凝聚物质物理学 凝聚物质物理学
- 统计力学 统计力学
- 机器学习 机器学习
背景情况:
- 阶段过渡的特点是系统对称性的变化.
- 识别这些对称性变化对于理解材料特性至关重要.
- 目前用于检测相位转换的方法可能是计算密集且不太准确的.
研究的目的:
- 引入一种新的深度神经网络 (DNN) 方法,即组等价自编码器 (GE自编码器),用于识别相位边界.
- 为了利用群理论来限制自动编码器,并学习对称不变的顺序参数.
- 提高相位转换检测的准确性,稳定性和效率.
主要方法:
- 利用群理论来识别不变对称性,并限制GE自编码器的参数.
- 在学习顺序参数等差的损失函数中纳入对称性规范化术语.
- 将GE自编码器应用于2D经典铁磁和反铁磁Ising模型.
主要成果:
- GE自编码器准确地确定了哪些对称性在不同温度下自发地断裂.
- 它估计了热力学极限中的临界温度,与基线自动编码器相比,具有更高的准确性,稳定性和时间效率.
- 该方法在检测外部破坏对称性的磁场方面表现出更高的灵敏度.
结论:
- GE自编码器提供了一种强大而高效的工具,用于检测相位过渡和分析自发对称性破坏.
- 这种DNN方法在准确性和计算性能方面比传统方法具有显著的优势.
- 该框架可适应用于研究各种表现出相位过渡和对称性变化的物理系统.
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