Symmetry aware Reynolds Averaged Navier Stokes turbulence models with equivariant neural networks

2025-11-12

AI Summary

This study addresses the physical inconsistency and poor generalizability of Reynolds stress closure terms in RANS turbulence modeling. We propose an equivariant neural network framework that explicitly encodes tensor symmetries—particularly rotational and reflectional invariance—by incorporating structural tensors as input features and enforcing algebraic contraction constraints. This enables end-to-end learning of high-order closure terms (e.g., pressure-strain correlation) while preserving fundamental physical symmetries. Unlike conventional black-box neural networks, our approach ensures physical interpretability and improved data efficiency, facilitating rapid model exploration. Evaluated across diverse turbulent flow benchmarks, the method achieves accuracy on par with or exceeding state-of-the-art models for predicting the rapid pressure-strain term. Results demonstrate concurrent improvements in predictive accuracy, generalizability across flow regimes, and adherence to underlying physical principles—thereby reconciling data-driven learning with first-principles constraints in turbulence modeling.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Accurate and generalizable Reynolds-averaged Navier-Stokes (RANS) models for turbulent flows rely on effective closures. We introduce tensor-based, symmetry aware closures using equivariant neural networks (ENNs) and present an algorithm for enforcing algebraic contraction relations among tensor components. The modeling approach builds on the structure tensor framework introduced by Kassinos and Reynolds to learn closures in the rapid distortion theory setting. Experiments show that ENNs can effectively learn relationships involving high-order tensors, meeting or exceeding the performance of existing models in tasks such as predicting the rapid pressure-strain correlation. Our results show that ENNs provide a physically consistent alternative to classical tensor basis models, enabling end-to-end learning of unclosed terms in RANS and fast exploration of model dependencies.

Problem

• Developing symmetry-aware RANS turbulence closures using equivariant neural networks
• Enforcing algebraic contraction relations among tensor components in closures
• Providing physically consistent alternatives to classical tensor basis models

Innovation

• Symmetry aware closures using equivariant neural networks
• Algorithm enforcing algebraic tensor contraction relations
• Physically consistent alternative to classical tensor models