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首页> 外文期刊>SIAM/ASA Journal on Uncertainty Quantification >Generative Stochastic Modeling of Strongly Nonlinear Flows with Non-Gaussian Statistics
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Generative Stochastic Modeling of Strongly Nonlinear Flows with Non-Gaussian Statistics

机译：基于非高斯统计的强非线性流的生成随机建模

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摘要

Strongly nonlinear flows, which commonly arise in geophysical and engineering turbulence, are characterized by persistent and intermittent energy transfer between various spatial and temporal scales. These systems are difficult to model and analyze due to combination of high dimensionality and uncertainty, and there has been much interest in obtaining reduced models, in the form of stochastic closures, which can replicate their non-Gaussian statistics in many dimensions. Here, we propose a data-driven framework to model stationary chaotic dynamical systems through nonlinear transformations and a set of decoupled stochastic differential equations (SDEs). Specifically, we use optimal transport to find a transformation from the distribution of time-series data to a multiplicative reference probability measure such as the standard normal distribution. Then we find the set of decoupled SDEs that admit the reference measure as the invariant measure, and also closely match the spectrum of the transformed data. As such, this framework represents the chaotic time series as the evolution of a stochastic system observed through the lens of a nonlinear map. We demonstrate the application of this framework in the Lorenz-96 system, a 10-dimensional model of high-Reynolds cavity flow, and reanalysis climate data. These examples show that SDE models generated by this framework can reproduce the non-Gaussian statistics of systems with moderate dimensions (e.g., 10 and more) and predict super-Gaussian tails that are not readily available from little training data. These findings suggest that this class of models provides an efficient hypothesis space for learning strongly nonlinear flows from small amounts of data.
机译：强烈非线性流动,通常出现在地球物理和工程湍流特点是持久和间歇不同空间和之间的能量转移时间尺度。由于高模型和分析维度和不确定性,有很多兴趣获得简化模型,随机闭包的形式,它可以在许多复制他们的非高斯统计数据维度。静止的混沌动力学框架模型通过非线性变换和系统解耦的随机微分方程(sd)。交通的转换时间序列数据的分布乘法引用概率测度标准正态分布。的解耦sd集承认的参考测量的不变测度密切匹配的频谱转换数据。代表了混沌时间序列的进化的随机系统的观察镜头的非线性映射。洛伦兹- 96应用程序的框架系统,high-Reynolds的十维模型空泡流,再分析气候数据。例子表明,空间数据模型生成框架可以复制的非高斯统计信息系统与温和的维度(例如,10和更多)和预测高斯没有现成的小尾巴训练数据。类的模型提供了一个有效的假说空间学习的强烈非线性流少量的数据。

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