Development of new models of turbulence in hydrodynamics and deep learning

MathAI 2025 Conference Submission27 Authors

01 Feb 2025 (modified: 22 Feb 2025)MathAI 2025 Conference Withdrawn SubmissionEveryoneRevisionsBibTeXCC BY 4.0
Keywords: Navier-Stokes equation, turbulence, hydrodynamics, gradient boosting, transformer
Abstract: Accuracy of the determination of integral parameters of the flow (Nusselt numbers and friction factor) via simulations of test cases (backward-facing step flow, channel flow and flow around the rod bundles) by new turbulence model must be better. Architectures have been developed and trained in various formulations of the turbulent viscosity restoration problem. The architectures have been trained and validated on various data sets. The most promising in terms of the final metric were 2 approaches. The approach using gradient boosting and the approach using the transformer network architecture. Next, for each of the problem, there will be feature importance graphs constructed through the "shap" value and using classical feature importance assessment algorithms (through split counting in the case of boosting), a value correlation table, graphs of the target value dependence on the values ​​in the incoming tuple. a graph of the error distribution and the values ​​of the metrics obtained on the validation data set. The metrics used were the root mean square deviation (RMSE), absolute deviation (MAE) and relative deviation (MAPE) of the target value from the predicted value. For each experiment, graphs of the target value dependence on each of the features were constructed section (Influence of features on the target variable). A graph of the distribution of the value predicted by the neural network and the true value was also constructed section (Distribution of predicted and true values). This is necessary to see the dependence of the algorithm's prediction errors on the range of the target variable in which we are located. Graphs of the importance of features and the correlation matrix between them were constructed section (Feature importance plot), this is necessary to interpret the model's predictions and determine which values ​​of the input variables had the greatest impact on the final prediction.
Submission Number: 27
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