Realisability-informed machine learning for turbulence anisotropy mappings
Why this work is in the frame
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Bibliographic record
Abstract
Within the context of machine learning-based closure mappings for Reynolds-averaged Navier Stokes turbulence modelling, physical realisability is often enforced using ad hoc postprocessing of the predicted anisotropy tensor. In this study, we address the realisability issue via a new physics-based loss function that penalises non-realisable results during training, thereby embedding a preference for realisable predictions into the model. Additionally, we propose a new framework for data-driven turbulence modelling which retains the stability and conditioning of optimal eddy viscosity-based approaches while embedding equivariance. Several modifications to the tensor basis neural network to enhance training and testing stability are proposed. We demonstrate the conditioning, stability and generalisation of the new framework and model architecture on three flows: flow over a flat plate, flow over periodic hills and flow through a square duct. The realisability-informed loss function is demonstrated to significantly increase the number of realisable predictions made by the model when generalising to a new flow configuration. Altogether, the proposed framework enables the training of stable and equivariant anisotropy mappings, with more physically realisable predictions on new data. We make our code available for use and modification by others. Moreover, as part of this study, we explore the applicability of Kolmogorov–Arnold networks to turbulence modelling, assessing its potential to address nonlinear mappings in the anisotropy tensor predictions and demonstrating promising results for the flat plate case.
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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