Data-driven prediction of large-scale spatiotemporal chaos with distributed low-dimensional models

TL;DR

This paper introduces a novel data-driven, low-dimensional modeling approach for large-scale spatiotemporal chaos, decomposing systems into local patches and employing autoencoders and neural ODEs to efficiently capture complex dynamics.

Contribution

The authors develop a parallel, patch-based modeling framework using autoencoders and neural ODEs to effectively model high-dimensional chaotic systems with reduced computational complexity.

Findings

Reduced state dimension by up to two orders of magnitude.

Accurately captures short-term dynamics and long-term statistics.

Applicable to complex systems like Kuramoto-Sivashinsky and 2D Kolmogorov flow.

Abstract

Complex chaotic dynamics, seen in natural and industrial systems like turbulent flows and weather patterns, often span vast spatial domains with interactions across scales. Accurately capturing these features requires a high-dimensional state space to resolve all the time and spatial scales. For dissipative systems the dynamics lie on a finite-dimensional manifold with fewer degrees of freedom. Thus, by building reduced-order data-driven models in manifold coordinates, we can capture the essential behavior of chaotic systems. Unfortunately, these tend to be formulated globally rendering them less effective for large spatial systems. In this context, we present a data-driven low-dimensional modeling approach to tackle the complexities of chaotic motion, Markovian dynamics, multi-scale behavior, and high numbers of degrees of freedom within large spatial domains. Our methodology involves a parallel scheme of decomposing a spatially extended system into a sequence of local `patches', and constructing a set of coupled, local low-dimensional dynamical models for each patch. Here, we choose to construct the set of local models using autoencoders (for constructing the low-dimensional representation) and neural ordinary differential equations, NODE, for learning the evolution equation. Each patch, or local model, shares the same underlying functions (e.g., autoencoders and NODEs) due to the spatial homogeneity of the underlying systems we consider. We apply this method to the Kuramoto-Sivashinsky equation and 2D Kolmogorov flow, and reduce state dimension by up to two orders of magnitude while accurately capturing both short-term dynamics and long-term statistics.