Abstract

This talk will introduce some of the prevailing trends in embedding physics into machine learning.

Machine learning has shown great potential in tackling challenging tasks in a variety of fields. However, training deep neural networks requires big data, not always available for scientific problems. Instead, one alternative approach is to utilize additional information based on the laws of physics to train these networks. Such physics-informed learning integrates (noisy) data and mathematical models, and implements them through neural networks or other kernel-based regression networks. Moreover, it may be feasible to design customized network architectures that inherently satisfy physical constraints, leading to enhanced accuracy, faster training and improved generalization.

References (recommended reading, not required):

Karniadakis, George Em, et al. “Physics-informed machine learning.” Nature Reviews Physics 3.6 (2021): 422-440.

Lu, Lu, et al.. “DeepXDE: A deep learning library for solving differential equations.” SIAM review, 2021.

Raissi, Maziar, Paris Perdikaris, and George E. Karniadakis. “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.” Journal of Computational physics 378 (2019): 686-707.

Lu, Lu, et al. “Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.” Nature machine intelligence 3.3 (2021): 218-229.

Kovachki, Nikola, et al. “Neural operator: Learning maps between function spaces.” arXiv preprint arXiv:2108.08481 (2021).

Li, Zongyi, et al. “Fourier neural operator for parametric partial differential equations.” arXiv preprint arXiv:2010.08895 (2020)