Symmetry aware Reynolds Averaged Navier Stokes turbulence models with equivariant neural networks
Aaron Miller, Sahil Kommalapati, Robert Moser, Petros Koumoutsakos
TL;DR
The paper develops symmetry‑aware Reynolds‑averaged turbulence closures by embedding tensor functions in equivariant neural networks (ENNs) and introducing an exact linear‑constraint layer. Grounded in the Kassinos–Reynolds RDT structure‑tensor framework, the approach learns closures for M, L, and J that depend on input tensors and, crucially, can incorporate nonlinear Q^* effects. Experimental results on rapid distortion theory data demonstrate state‑of‑the‑art accuracy, with ENNs outperforming tensor‑basis methods while enforcing physical symmetries and linear contractions exactly. The method removes the need to pre‑derive tensor bases and enables flexible exploration of model dependencies within a rigorous symmetry‑preserving setting, with potential extension to full RANS solvers and broader tensor‑function problems.
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.