Symmetry-aware Reynolds-averaged turbulence modeling with equivariant neural networks

We introduce equivariant neural networks (ENNs) for representing tensor function closures for RANS. We present a novel decoding technique that enables an additional class of tensor constraints to be enforced exactly, alongside equivariance and index permutation symmetries. Building on the structure tensor framework of Kassinos and Reynolds, the present method is used to learn several closure models in the rapid distortion theory setting. Our results show that ENNs can effectively learn relationships involving high-order tensors, meeting or exceeding the performance of existing models on tasks such as predicting the rapid pressure-strain correlation. These results suggest that ENNs offer a symmetry-consistent alternative to traditional tensor basis models. They enable automated, end-to-end learning of unclosed terms in RANS and fast exploration of model dependencies.