Semi-supervised GAN with sparse ground truth as Boundary Conditions
Résumé
Often, physical phenomena are difficult to model by a simple equation and require a lot of processing resources. Studies on Physics-Informed Neural Networks (PINNs) have repeatedly shown the interest of leveraging the information contained in context-relevant physics equations in order to guide the training, as well the ability of this type of networks to reduce the need for labeled data. Some of these analysis have also demonstrated the interest of additional knowledge through Initial and Boundary Conditions (I/BCs) in this type of context. This knowledge can take a variety of forms and shapes, among which is the one of sparse ground truths, and more precisely sparse matrices, as matrices are often well fitted to represent the spatial aspect of this type of problem. The popularity of Computer Vision techniques is partly due to their ability to take into account the spatial aspect of a given problem. The combined use of methods from these two fields therefore seems natural. This paper introduces a method for the use of Boundary Conditions for Generative Adversarial Networks (GANs), and outside the context of PINNs. The interest of leveraging the BCs with a GAN is evaluated in terms of performance, and various BC configuration and quantities are tested to discuss their impact on obtained performance.