Physically Interpretable Representation and Controlled Generation for Turbulence Data

TL;DR

This paper introduces a Gaussian Mixture Variational Autoencoder that encodes high-dimensional turbulence data into interpretable, physically meaningful low-dimensional representations, enabling controlled generation and improved understanding of fluid flow behaviors.

Contribution

It proposes a novel GMVAE-based framework for physically interpretable data encoding and introduces a graph spectral metric for assessing representation smoothness.

Findings

Enhanced clustering of flow regimes based on Reynolds number

Improved physical interpretability of latent space

Robust generation of turbulence data across flow conditions

Abstract

Computational Fluid Dynamics (CFD) plays a pivotal role in fluid mechanics, enabling precise simulations of fluid behavior through partial differential equations (PDEs). However, traditional CFD methods are resource-intensive, particularly for high-fidelity simulations of complex flows, which are further complicated by high dimensionality, inherent stochasticity, and limited data availability. This paper addresses these challenges by proposing a data-driven approach that leverages a Gaussian Mixture Variational Autoencoder (GMVAE) to encode high-dimensional scientific data into low-dimensional, physically meaningful representations. The GMVAE learns a structured latent space where data can be categorized based on physical properties such as the Reynolds number while maintaining global physical consistency. To assess the interpretability of the learned representations, we introduce a novel metric based on graph spectral theory, quantifying the smoothness of physical quantities along the latent manifold. We validate our approach using 2D Navier-Stokes simulations of flow past a cylinder over a range of Reynolds numbers. Our results demonstrate that the GMVAE provides improved clustering, meaningful latent structure, and robust generative capabilities compared to baseline dimensionality reduction methods. This framework offers a promising direction for data-driven turbulence modeling and broader applications in computational fluid dynamics and engineering systems.