  As applications of deep learning (DL) continue to seep into critical
scientific use-cases, the importance of performing uncertainty quantification
(UQ) with DL has become more pressing than ever before. In scientific
applications, it is also important to inform the learning of DL models with
knowledge of physics of the problem to produce physically consistent and
generalized solutions. This is referred to as the emerging field of
physics-informed deep learning (PIDL). We consider the problem of developing
PIDL formulations that can also perform UQ. To this end, we propose a novel
physics-informed GAN architecture, termed PID-GAN, where the knowledge of
physics is used to inform the learning of both the generator and discriminator
models, making ample use of unlabeled data instances. We show that our proposed
PID-GAN framework does not suffer from imbalance of generator gradients from
multiple loss terms as compared to state-of-the-art. We also empirically
demonstrate the efficacy of our proposed framework on a variety of case studies
involving benchmark physics-based PDEs as well as imperfect physics. All the
code and datasets used in this study have been made available on this link :
https://github.com/arkadaw9/PID-GAN.

Machine Learning;Machine Learning