Field Inversion and Machine Learning With Embedded Neural Networks: Physics-Consistent Neural Network Training

摘要

Recent years have seen a substantial effort towards the use of data to augment physical models to improve predictive accuracy. The Field Inversion and Machine Learning (FIML) approach [1] is one such method that uses statistical inference to extract spatio-temporal model discrepancies and machine learning to reconstruct the discrepancies into functional forms that are embedded within physical models. While the inference step in FIML addresses discrepancies between the model outputs and data in a consistent manner, there are no guarantees that the inferred discrepancies are learnable. Imperfect learning can result in an inconsistency between the information extracted in the inference step and the model augmentation. The present work builds on the FIML framework by integrating the inference and learning in a self-consistent manner. Additionally, by integrating learning in the inverse problem, numerous datasets can be considered simultaneously, promoting improved generalization of the resulting model augmentation. The methodology is demonstrated by producing a model augmentation that improves RANS predictions for airfoils at high angles of attack. It is shown that this augmentation improves predictions of quantities of interest that were not present in the data, and on geometries that were not included in the training. The entire framework is implemented in the SU2 solver and open sourced for use by the community.