  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.
