A data-driven statistical-stochastic surrogate modeling strategy for complex nonlinear non-stationary dynamics
A data-driven statistical-stochastic surrogate modeling strategy for complex nonlinear non-stationary dynamics
复制标题
复杂非线性非平稳动力学的数据驱动统计随机代理建模策略
DOI：
10.1016/j.jcp.2023.112085
复制
发表时间：
2023
影响因子：
4.1
通讯作者：
Harlim, John
中科院分区：
文献类型：
--
作者：
Qi, Di;Harlim, John
我们提出了一种统计随机代理建模方法来预测在各种初始条件和外部强迫扰动下的均值和方差统计的响应。所提出的建模框架扩展了纯统计建模方法，这种方法实际上仅限于高维状态变量的同质统计体系。新的封闭制度使人们能够克服在非同质统计制度中出现的几个实际问题。首先，所提出的集成模型将平均统计量和随机波动相结合，自然产生正定协方差矩阵估计，这是一个具有挑战性的问题，阻碍了纯统计建模方法。其次，所提出的闭包模型为未解决的通量嵌入了一个非马尔可夫神经网络模型，使得动力学的方差是一致的，克服了随机波动动力学固有的不稳定性。该框架有效地将未解决动力学的经典随机参数化建模范式扩展为具有残余长短期记忆神经网络结构的半参数化模型。第三，基于经验信息度量，我们通过拟合衡量响应统计差异的损失函数，提供了一个高效和有效的训练过程。给出了具有齐次和非齐次统计机制的混沌动力学特征的ODEs系统Lorenz-96模型的数值实例。在后一种情况下，我们将看到统计预测的有效性，即使对应于领先平均能量和方差谱的解析傅立叶模式不一致。
We propose a statistical-stochastic surrogate modeling approach to predict the response of the mean and variance statistics under various initial conditions and external forcing perturbations. The proposed modeling framework extends the purely statistical modeling approach that is practically limited to the homogeneous statistical regime for high-dimensional state variables. The new closure system allows one to overcome several practical issues that emerge in the non-homogeneous statistical regimes. First, the proposed ensemble modeling that couples the mean statistics and stochastic fluctuations naturally produces positive-definite covariance matrix estimation, which is a challenging issue that hampers the purely statistical modeling approaches. Second, the proposed closure model, which embeds a non-Markovian neural-network model for the unresolved fluxes such that the variance of the dynamics is consistent, overcomes the inherent instability of the stochastic fluctuation dynamics. Effectively, the proposed framework extends the classical stochastic parametric modeling paradigm for the unresolved dynamics to a semi-parametric parameterization with a residual Long-Short-Term-Memory neural network architecture. Third, based on empirical information metric, we provide an efficient and effective training procedure by fitting a loss function that measures the differences between response statistics. Supporting numerical examples are provided with the Lorenz-96 model, a system of ODEs that admits the characteristic of chaotic dynamics with both homogeneous and inhomogeneous statistical regimes. In the latter case, we will see the effectiveness of the statistical prediction even though the resolved Fourier modes corresponding to the leading mean energy and variance spectra do not coincide.
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DOI：
10.1073/pnas.1313065110
发表时间：
2013-08-20
影响因子：
11.1
作者：
Sapsis, Themistoklis P.;Majda, Andrew J.
通讯作者：
Majda, Andrew J.
非马尔可夫时间序列的基于核的预测
DOI：
10.1016/j.physd.2020.132829
发表时间：
2021
期刊：
Physica D: Nonlinear Phenomena
影响因子：
--
作者：
Gilani, Faheem;Giannakis, Dimitrios;Harlim, John
通讯作者：
Harlim, John
线性和非线性统计响应理论以及复杂湍流动力系统的灵敏度分析和统计控制的原型应用。
影响因子：
2.9
作者：
A. Majda;D. Qi
通讯作者：
D. Qi
用于预测复杂湍流动力系统中的统计响应和不确定性量化的降阶模型策略
影响因子：
10.2
作者：
A. Majda;D. Qi
通讯作者：
D. Qi
用于复杂湍流系统集合预测的物理信息数据驱动算法
DOI：
10.1016/j.amc.2023.128480
发表时间：
2022
期刊：
Appl. Math. Comput.
影响因子：
--
作者：
N. Chen;D. Qi
通讯作者：
D. Qi