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可解释的神经网络量子状态,用于解决非线性施罗丁格方程的稳定状态
1Hebei Key Laboratory of Physics and Energy Technology, Department of Mathematics and Physics, North China Electric Power University, Baoding, Hebei 071003, China.
Chaos (Woodbury, N.Y.)
|November 18, 2025
概括
我们介绍了一个神经网络量子状态 (NNQS) 方法来解决非线性施罗丁格方程 (NLSE). 这种方法准确计算了激发状态,克服了非线性波现象的传统技术的局限性.
科学领域:
- 计算物理 计算物理
- 机器学习应用 机器学习应用
- 非线性动力学是一种非线性动力学.
背景情况:
- 非线性施罗丁格方程 (NLSE) 对于理解各种科学领域的非线性波现象至关重要.
- 计算激发状态的NLSE是计算上具有挑战性的,因为诸如非线性引入的非正规性等问题.
- 现有的方法,如想象时间进化,对于基本状态是有效的,但对于激发状态是不够的.
研究的目的:
- 开发一种新的计算方法,用于确定非线性施罗丁格方程的基本和激发状态.
- 解决传统方法在处理非线性诱导的非正规性方面的局限性.
- 建立基于机器学习的框架,用于分析复杂的混乱波系统.
主要方法:
- 提出了一个神经网络量子状态 (NNQS) 方法,利用神经网络参数化波函数.
- 直接最大限度地降低了功能的能量,使得基本和激发状态的计算成为可能.
- 设计了紧和可解释的神经网络架构,以实现解决方案的分析近似.
主要成果:
- 使用NNQS方法成功计算了非线性施罗丁格方程的基态和激态.
- 证明了NNQS通过可解释的网络设计提供解决方案的分析近似的能力.
- 应用该方法来分析NLSE的时空混乱,有效地捕捉复杂的混乱动态.
结论:
- 神经网络量子状态 (NNQS) 方法为计算非线性施罗丁格方程的激发状态提供了一个强大的解决方案.
- 这项工作验证了NNQS作为桥梁机器学习和理论物理学的强大工具,用于研究混乱波系统.
- 开发的方法有助于更深入地了解复杂的非线性波现象及其相关的混乱动态.
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