使用神经网络和短轨迹数据预测罕见事件.
John Strahan1, Justin Finkel2, Aaron R Dinner1,3
1Department of Chemistry and James Franck Institute, the University of Chicago, Chicago, IL 60637.
Journal of computational physics
|June 19, 2023
概括
在复杂系统中预测罕见事件是具有挑战性的. 这项研究引入了一个神经网络方法来解决费曼-卡克方程,使得从短模拟数据准确的统计预测,即使是高维模型.
科学领域:
- 计算科学 计算科学
- 应用数学 应用数学 应用数学
- 大气科学 大气科学
背景情况:
- 对罕见事件统计的准确估计对于建模随机动态系统至关重要.
- 由于时间尺度不匹配,对于罕见事件,直接模拟通常是不可行的.
- 费曼-卡克方程为计算这些统计数据提供了一个强大的框架.
研究的目的:
- 开发一种使用神经网络解决费曼-卡克方程的新方法.
- 为了在复杂的系统中准确预测罕见事件统计数据.
- 为了证明该方法对高维模型和观测数据的适用性.
主要方法:
- 在短轨迹数据上训练神经网络,以近似解决费曼-卡克方程.
- 采用马尔科夫近似而不假设底层模型动态.
- 制定适应性抽样策略,以有效获取数据.
主要成果:
- 神经网络方法准确地解决了罕见事件统计的费曼-卡克方程.
- 该方法适用于复杂的计算模型和观测数据.
- 准确的统计数据被计算为一个75维的平流层突然变暖模型.
结论:
- 对费曼-卡克方程的基于神经网络的解决方案为罕见事件统计提供了有效的方法.
- 该方法为复杂的动态系统提供了灵活而强大的工具.
- 这种技术提高了在各种科学领域模拟和预测罕见现象的能力.
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