Robustness-based training and explainability of a data-driven model to cure the inconsistency between RANS and DNS datasets

The present study proposes the use of Machine Learning to model turbulent heat transfer in liquid metal cooled nuclear reactors. Traditional modelling methods are found to have limitations, and the availability of high-fidelity data for low Prandtl number fluids motivates the use of advanced regression techniques. The work is based on the analysis and the extension of the data-driven model developed by M. Fiore to simulate liquid metal heat transfer. The original Neural Network model was trained with high-fidelity data only. This approach was found to be limiting when the model is coupled with common momentum Reynolds Averaged Navier Stokes (RANS) closures due to the inconsistency between Direct Numerical Simulation (DNS) and RANS turbulence input data. In particular, the accuracy of the data-driven model dramatically decays when the network is applied in combination with momentum models based on the Boussinesq hypothesis e.g. the k-epsilon turbulence model. Datasets obtained from RANS simulations and DNS for the same flow conditions were compared and dimensional reduced with a Principal Component Analysis (PCA) algorithm. An artificial neural network model for turbulent heat flux prediction was trained using the PyTorch framework. The accuracy of the predictions is evaluated through a loss function that considers the results from both input datasets, with the Pareto front constructed from multiple training runs. This analysis showed the possibility to train a network that is able to identify the nature of the input database and gave reasonable predictions with both sets of input data. An a priori and a posteriori validation were carried out to test the model's performances. In particular, the newly trained network was implemented in OpenFoam, a Computational Fluid Dynamic (CFD) software. Finally, an interpretability analysis with the Shapley values algorithm was performed to understand the peculiarity of the models trained with hybrid DNS-RANS input datasets.