多级化储计算学习了使用莱维噪声的噪声诱导过渡
Zequn Lin1,2, Jürgen Kurths3,4,5, Ying Tang6,7
1Department of Physics, Fudan University, Shanghai 200433, China.
Chaos (Woodbury, N.Y.)
|July 18, 2025
概括
这项研究表明,多尺度储计算有效地模拟了复杂的随机系统中的噪声诱导过渡. 该框架准确地预测过渡统计数据,即使有非高斯噪声.
科学领域:
- 随机动态系统 随机动态系统
- 复杂系统理论 复杂系统理论
- 机器学习应用 机器学习应用
背景情况:
- 噪音诱导的过渡在随机系统中是基本的,但在非高斯噪音或复杂的动态中变得复杂.
- 了解这些转变在物理学,生物学和工程学中至关重要.
研究的目的:
- 应用多级化水库计算框架来学习和建模噪声诱导的过渡.
- 调查框架在具有非高斯噪声 (莱维) 和复杂动态 (极限周期) 的系统上的有效性.
主要方法:
- 使用一个多尺度的水库计算框架.
- 在呈现噪声诱导过渡的轨迹上训练模型.
- 专注于带有Lévy噪声的可视化系统和带有高斯噪声的极限循环系统.
主要成果:
- 多级化储计算框架成功生成了捕获过渡统计数据的数据.
- 过渡间隔和概率分布的预测与测试数据密切匹配.
- 该模型证明了对突然的噪音转移和振荡动态的概率捕捉.
结论:
- 多尺度储计算是分析一般随机系统的强大工具.
- 该框架对研究诸如噪声诱导过渡等复杂现象具有前景.
- 这种方法为了解各种科学领域的随机动力学提供了新的途径.
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