Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural phenomena makes it extremely challenging to develop full-order models (FOMs) and apply them to studying many quantities of interest. In contrast, appropriate reduced-order models (ROMs) are favored due to their high computational efficiency and ability to describe the key dynamics and statistical characteristics of natural phenomena. Taking the viscous Burgers equation as an example, this paper constructs a Convolutional Autoencoder-Reservoir Computing-Normalizing Flow algorithm framework, where the Convolutional Autoencoder is used to construct latent space representations, and the Reservoir Computing-Normalizing Flow framework is used to characterize the evolution of latent state variables. In this way, a data-driven stochastic parameter reduced-order model is constructed to describe the complex system and its dynamic behavior.

中文翻译：

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基于混合机器学习方法的随机参数降阶模型

为自然现象中的复杂系统建立适当的数学模型不仅有助于加深我们对自然的理解，而且还可以用于状态估计和预测。然而，自然现象的极端复杂性使得开发全阶模型（FOM）并将其应用于研究许多感兴趣的数量变得极具挑战性。相比之下，适当的降阶模型（ROM）因其高计算效率和描述自然现象的关键动力学和统计特征的能力而受到青睐。以粘性Burgers方程为例，构建了卷积自编码器-储层计算-归一化流算法框架，其中卷积自编码器用于构造潜在空间表示，储层计算-归一化流框架用于表征演化潜在状态变量。这样，就构建了数据驱动的随机参数降阶模型来描述复杂系统及其动态行为。