Augmenting mesh-based data-driven models with physics gradients

Abstract

Deep learning technologies are increasingly used in various applications, with significant potential in aerospace for reduced-order modelling due to their ability to handle nonlinear systems. The effectiveness of data-driven methods relies on the adequacy and volume of training data, which poses a challenge in a design environment. To address this, physics-informed machine learning, which integrates physics knowledge into data-driven frameworks, has emerged as a promising solution. Directly applying physics terms to aircraft surfaces is complex, so this study utilizes solution gradients to effectively capture flow features. We introduce a hybrid framework that combines geometric deep learning with gradient terms, building on a previous data-driven approach for aerodynamic modelling on large-scale, three-dimensional unstructured grids. We evaluated various hybrid schemes to enhance prediction accuracy. Two gradient-enhanced approaches were found to outperform the purely data-driven model: the first integrates output differentiation into the training loss, achieving the highest accuracy at an increased training cost; the second employs a masking technique to weight regions with large gradients, providing a reasonable accuracy improvement at a lower training cost. This study focuses on predicting distributed aerodynamic loads around the NASA Common Research Model wing/body configuration under various transonic flight conditions. Our findings show that incorporating gradient information into deep learning models significantly improves the accuracy of the predictions and can compensate for a smaller dataset without compromising accuracy. Furthermore, the approaches proposed herein are directly applicable to any problem with discretised spatial domain.