使用随机批量方法的高阶时刻关闭模型,用于高效计算多尺度流系统
1Department of Mathematics, Purdue University, 150 North University Street, West Lafayette, Indiana 47907, USA.
Chaos (Woodbury, N.Y.)
|October 23, 2023
概括
我们使用随机批量方法 (RBM) 开发了一种高阶随机-统计时刻闭合模型,用于高效的流系统预测. 这种方法准确地捕获复杂的统计数据和极端事件,并降低了计算成本.
科学领域:
- * 计算流体动力学
- * 应用数学 * 应用数学
- * 统计建模 * 统计建模
背景情况:
- * 多级复杂的流系统在准确的统计时刻和概率密度函数预测方面存在挑战.
- * 传统的集体模拟在计算上昂贵,特别是对于具有密切结合的时空尺度的高维系统.
- * 建模非高斯统计和极端事件需要先进的闭包模型.
研究的目的:
- * 提出一个高阶随机-统计时刻关闭模型,以实现高效的集体预测.
- * 引入计算策略,特别是随机批量方法 (RBM),以减少组件大小和计算成本.
- * 通过将小规模波动与主导模式联系起来,为高维系统开发一个减少顺序模型.
主要方法:
- * 开发一个高阶随机统计时刻关闭模型.
- * 实施随机批量方法 (RBM) 以实现高效的组合模拟.
- *创建一个减少顺序模型,将小规模波动模式与主导组合模式联系起来.
- *使用单层和双层Lorenz '96系统进行验证.
主要成果:
- * RBM模型准确地捕获了前排统计数据和非高斯概率分布.
- *与直接蒙特卡洛方法相比,计算成本大幅降低.
- * 完全和减少顺序的RBM模型都显示出高预测能力.
- *有效处理混乱的特征和多样化的统计制度.
结论:
- * 建议使用RBM的高阶随机统计时刻闭合模型,为流系统预测提供了一种高效的方法.
- *这些模型成功地捕捉了复杂的统计现象,包括极端事件.
- *这些模型为预测,不确定性量化和数据同化在各种应用中提供了有价值的工具.
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