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

Area of Science:

• Computational physics
• Fluid dynamics
• Machine learning

Background:

• Spatiotemporal chaos in systems like turbulent flows often exists on finite-dimensional attractors.
• High dimensionality of these attractors necessitates large datasets for training reduced-order models.
• Domain size in large-scale systems often leads to a linear increase in attractor dimension, posing a challenge.

Purpose of the Study:

• To develop a framework for constructing local reduced-order models by decomposing spatially extended systems.
• To overcome the data burden associated with high dimensionality in complex systems.
• To enable accurate modeling of systems with spatiotemporal chaos.

Main Methods:

• Decomposing spatially extended systems into local patches.
• Utilizing autoencoders for dimension reduction within each patch.
• Employing neural ordinary differential equations for local temporal dynamics learning.

Main Results:

• Successfully applied the framework to the Kuramoto-Sivashinsky equation and 2D Kolmogorov flow.
• Achieved dimension reduction by up to two orders of magnitude.
• Accurately captured both short-term dynamics and long-term statistics of the systems.

Conclusions:

• The developed framework effectively constructs local reduced-order models for spatially extended systems.
• This approach significantly reduces dimensionality while maintaining accuracy in modeling complex dynamics.
• The framework has broad applicability to dissipative partial differential equations in physics and engineering.