Spectrally informed learning of fluid flows.

Area of Science:

• Fluid dynamics
• Computational physics
• Machine learning

Background:

• Accurate fluid flow models are crucial for geophysical, aerodynamic, and biological systems.
• High-dimensional fluid flow data often contains underlying low-rank structures representing bulk motion.
• Extracting these low-rank dynamics parsimoniously from data is a significant challenge.

Purpose of the Study:

• To develop a novel method for extracting low-rank models of fluid flows.
• To leverage known spectral properties within a machine learning framework.
• To improve the accuracy and physical relevance of fluid flow models.

Main Methods:

• A spectrally informed approach integrating known spectral properties into the learning process.
• Imposing regularizations on learned dynamics to prioritize low-frequency, high-power structures.
• Utilizing physics-informed machine learning principles.

Main Results:

• Demonstrated effectiveness in improving prediction accuracy for fluid flow models.
• Generated learned models that align better with the underlying spectral properties of flows.
• Successfully extracted parsimonious representations of low-rank dynamics.

Conclusions:

• The spectrally informed method offers a powerful way to extract meaningful low-rank dynamics from complex fluid flows.
• This approach enhances model prediction and ensures better adherence to physical spectral characteristics.
• It provides a more efficient and accurate way to model multiscale fluid phenomena.