Journal of Philosophical Transactions of the Royal Society, In Press, 2020
Authors - K. Kashinath, M. Mustafa, A. Albert,J-L. Wu, C. Jiang, S. Esmaeilzadeh ,K. Azizzadenesheli, R. Wang, A.Singh, A. Manepalli, D. Chirila, R.Yu, R. Walters, B. White, H. Xiao, H. A. Tchelepi, P. Marcus, A. Anandkumar, and Prabhat
Abstract - Deep learning (DL) provides novel and powerful ways of accurately and efficiently recognizing complex patterns, emulating the behavior of nonlinear physical systems, and predicting their spatio-temporal dynamics. Off-the-shelf DL models, however, do not necessarily obey the fundamental governing laws of physical systems, nor do they generalize well to scenarios on which they have not been trained. We survey, through multiple case studies, systematic and novel approaches to incorporating physics and domain knowledge into deep learning models designed to: emulate physical processes; downscale coarse data; and forecast the spatio-temporal evolution of processes relevant to weather and climate modeling. These approaches develop new, custom-designed architectures of neural networks and implement physics-based regularization. We show that these techniques achieve physical consistency, reduce the time required for training, improve data efficiency, and are scalable. Finally, we highlight current limitations and challenges of physics-informed DL models, and opportunities for the future.
Keywords: Deep Learning, PDEs, Physics-Constrained