Deep structured neural networks for turbulence closure modeling
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Despite well-known limitations of Reynolds-averaged Navier–Stokes (RANS) simulations, this methodology remains the most widely used tool for predicting many turbulent flows due to computational efficiency. Machine learning is a promising approach to improve the accuracy of RANS simulations. One major area of improvement is using machine learning models to represent the complex relationship between the mean flow field gradients and the Reynolds stress tensor. In the present work, modifications to improve the stability of previous optimal eddy viscosity approaches for RANS simulations are presented and evaluated. The optimal eddy viscosity is reformulated with a non-negativity constraint, which promotes numerical stability. We demonstrate that the new formulation of the optimal eddy viscosity improves conditioning of RANS equations for a periodic hills test case. To demonstrate the suitability of this proportional/orthogonal tensor decomposition for use in a physics-informed data-driven turbulence closure, we use two neural networks (structured on this specific tensor decomposition, which is incorporated as an inductive bias into the network design) to predict the newly reformulated linear and non-linear parts of the Reynolds stress tensor. Injecting these network model predictions for the Reynolds stresses into RANS simulation improves predictions of the velocity field, even when compared to a sophisticated (state of the art) physics-based turbulence closure model. Finally, we apply shapley additive explanations values to obtain insights from the learned representation for inner workings of the neural network used to predict the optimal eddy viscosity from the input feature data.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it