在随机系统中以数据驱动发现逃逸现象
Jiangyan Liu1, Jiaqian Zhao1, Ming Yi1
1School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China.
Chaos (Woodbury, N.Y.)
|May 20, 2025
概括
这项研究引入了一种新的基于物理学的神经网络框架,用于分析随机系统中的逃逸现象. 它准确地计算了平均退出时间和逃脱概率,克服了传统方法的局限性.
科学领域:
- 动态系统和混沌理论
- 计算物理 计算物理
- 随机过程 随机过程
背景情况:
- 随机动态系统在物理学,生物学和金融学中至关重要,但它们的复杂行为,特别是逃生现象,难以分析.
- 传统的数值方法 (有限差异,有限元素,有限体积,蒙特卡罗) 在计算逃脱特征时,与高维系统和不规则域进行斗争,例如平均退出时间和逃脱概率.
研究的目的:
- 开发使用物理信息神经网络 (PINNs) 的无网格框架,用于分析布朗运动驱动的随机系统中的逃逸现象.
- 解决传统方法在高维和不规则领域的局限性,以计算平均退出时间和逃脱概率.
- 通过解决前向和反向问题,从逃逸数据中学习随机动力学.
主要方法:
- 提出了一个基于物理信息的神经网络 (PINNs) 的综合框架.
- 应用PINN方法来解决与随机系统中逃逸现象相关的前向和反向问题.
- 该方法避免了网格生成,可以自然处理不规则的域,并提供更好的计算效率和准确性.
主要成果:
- 拟议的PINN框架有效地计算了随机系统中的平均退出时间和退出概率.
- 与传统的数值方法相比,它表现出优越的性能,特别是在复杂的场景中.
- 数字示例证实了基于PINN的方法对分析逃逸特征和学习随机动态的准确性和有效性.
结论:
- 基于物理学的神经网络为研究随机动态系统中的逃逸现象提供了强大而多功能工具.
- 这种无网格的方法比传统的数值技术有了显著的进步,提高了计算效率和准确性.
- 该框架能够从逃逸数据中学习随机动态,这为复杂系统分析研究开辟了新的途径.
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