(518c) Distributed Low-Dimensional Models for Predicting Large Spatiotemporally Chaotic Dynamical Systems

Fluid flows are characterized by a chaotic motion, a large number of degrees of freedom, and a multi-scale nature in both space and time. With the availability of large sets of data through image analysis and high-performance computing, research has focused on developing data-driven Reduced-Order Models (ROMs) to accurately capture flow dynamic. However, data-driven models face challenges when dealing with high dimensionality, unknown physics lows, and nonlinearity. These factors make it difficult to effectively model the underlying dynamics of those systems and extract meaningful insights from data. This study aims to use machine learning techniques to predict spatially large fluid dynamics highly chaotic systems. As the domain increases, ROMs become more challenging, resulting in the worsening of the model performance and the increase of computational feasibility. We propose a solution to this problem by considering localized spatial regions, ‘chunks’, as separate dynamical systems that are equivalent and communicate with one another. Here, we target the two-dimensional Kolmogorov flow, and we significantly reduce the high-dimensional nature of the state space, via autoencoders, and NODEs for the spatio-temporal forecasting of the latent space. This methodology, referred to as Data-driven Manifold Dynamics (DManD), provides the ability to capture accurately the system dynamics in terms of short-time tracking and long-time statistics.