PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physics
This addresses uncertainty quantification for scientific applications using physics-informed deep learning, but it appears incremental as it builds on existing GAN and PIDL methods.
The paper tackles the problem of uncertainty quantification in physics-informed deep learning by proposing PID-GAN, a GAN framework that uses physics to inform both generator and discriminator, showing it avoids gradient imbalance issues and demonstrating efficacy on benchmark PDEs and imperfect physics.
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.