Physically Interpretable Representation and Controlled Generation for Turbulence Data

2025-01-31

AI Summary

High-dimensional turbulent CFD simulations face prohibitive computational costs, scarce data, and a lack of physically interpretable low-dimensional representations. Method: We propose a physics-driven, interpretable latent-space modeling framework. It introduces, for the first time, a graph-spectral-theory-based smoothness metric for physical quantities on the latent manifold and integrates it with a Gaussian Mixture Variational Autoencoder (GMVAE) to achieve structured clustering of the latent space according to key physical parameters—e.g., Reynolds number—ensuring global physical consistency. Results: Evaluated on multi-Reynolds-number 2D Navier–Stokes simulations of flow around a cylinder, the framework significantly improves clustering quality and generative robustness. The resulting low-dimensional representations enable high-fidelity reconstruction while providing explicit physical interpretability—outperforming state-of-the-art dimensionality reduction baselines across multiple quantitative metrics.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Computer Vision: Low Level & Physics-based Vision
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• High-dimensional turbulence data interpretation
• Physical consistency in data representation
• Efficient data-driven simulation methods

Innovation

• GMVAE encodes high-dimensional data
• Structured latent space based on physics
• Graph spectral theory assesses interpretability