{"ID":2879061,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.16891","arxiv_id":"2508.16891","title":"Quantifying Out-of-Training Uncertainty of Neural-Network based Turbulence Closures","abstract":"Neural-Network (NN) based turbulence closures have been developed for being used as pre-trained surrogates for traditional turbulence closures, with the aim to increase computational efficiency and prediction accuracy of CFD simulations. The bottleneck to the widespread adaptation of these ML-based closures is the relative lack of uncertainty quantification (UQ) for these models. Especially, quantifying uncertainties associated with out-of-training inputs, that is when the ML-based turbulence closures are queried on inputs outside their training data regime. In the current paper, a published algebraic turbulence closure1 has been utilized to compare the quality of epistemic UQ between three NN-based methods and Gaussian Process (GP). The three NN-based methods explored are Deep Ensembles (DE), Monte-Carlo Dropout (MCD), and Stochastic Variational Inference (SVI). In the in-training results, we find the exact GP performs the best in accuracy with a Root Mean Squared Error (RMSE) of $2.14 \\cdot 10^{-5}$ followed by the DE with an RMSE of $4.59 \\cdot 10^{-4}$. Next, the paper discusses the performance of the four methods for quantifying out-of-training uncertainties. For performance, the Exact GP yet again is the best in performance, but has similar performance to the DE in the out-of-training regions. In UQ accuracy for the out-of-training case, SVI and DE hold the best miscalibration error for one of the cases. However, the DE performs the best in Negative Log-Likelihood for both out-of-training cases. We observe that for the current problem, in terms of accuracy GP \u003e DE \u003e SV I \u003e MCD. The DE results are relatively robust and provide intuitive UQ estimates, despite performing naive ensembling. In terms of computational cost, the GP is significantly higher than the NN-based methods with a $O(n^3)$ computational complexity for each training step","short_abstract":"Neural-Network (NN) based turbulence closures have been developed for being used as pre-trained surrogates for traditional turbulence closures, with the aim to increase computational efficiency and prediction accuracy of CFD simulations. The bottleneck to the widespread adaptation of these ML-based closures is the rela...","url_abs":"https://arxiv.org/abs/2508.16891","url_pdf":"https://arxiv.org/pdf/2508.16891v1","authors":"[\"Cody Grogan\",\"Som Dhulipala\",\"Mauricio Tano\",\"Izabela Gutowska\",\"Som Dutta\"]","published":"2025-08-23T03:43:40Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"physics.flu-dyn\"]","methods":"[]","has_code":false}