(Must Read) Papers
M. Raissi, P. Perdikaris, and G.E. Karniadakis, Journal of Computational Physics, Volume 378, 2019, Pages 686-707, ISSN 0021-9991, https://doi.org/10.1016/j.jcp.2018.10.045.
Physics-informed Machine Learning
George Em Karniadakis, Ioannis G. Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang and Liu Yang, Nature Reviews Physics, 3, 422–440 (2021)
Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next
Cuomo, S., Di Cola, V.S., Giampaolo, F., Rozza, G., Raissi, M. and Piccialli, F., Journal of Scientific Computing, 92, 88 (2022)
Ameya D. Jagtap and George Em Karniadakis, Communications in Computational Physics, Vol. 28, No. 5, pp. 2002-2041, 2020. [GitHub]
Learning Nonlinear Operators via DeepONet based on the Universal Approximation Theorem of Operators
Lu, L., Jin, P., Pang, G., Zhang Z., and Karniadakis, G., Nature Machine Intelligence, 3, 218–229 (2021), https://doi.org/10.1038/s42256-021-00302-5
Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains, NeurIPS 2020 or arXiv
Matthew Tancik, Pratul P. Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan T. Barron, Ren Ng
Sifan Wang, Hanwen Wang, and Paris Perdikaris, Computer Methods in Applied Mechanics and Engineering, 2021
Fourier Neural Operator for Parametric Partial Differential Equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar, https://doi.org/10.48550/arXiv.2010.08895
Physics-informed Neural Networks (PINNs) for Fluid Mechanics: A Review
Shengze Cai, Zhiping Mao, Zhicheng Wang, Minglang Yin & George Em Karniadakis, Acta Mechanica Sinica, 37, 1727-1738 (2021)
Physics-informed Neural Networks for Heat Transfer Problems
Shengze Cai, Zhicheng Wang, Sifan Wang, Paris Perdikaris, George Em Karniadakis, ASME Journal of Heat and Mass Transfer, 143(6), 060801 (2021)
Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
Sifan Wang, Yujun Teng, and Paris Perdikaris, SIAM Journal on Scientific Computing, 43(5), A3033-S907 (2020)
PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs
Zhongkai Hao, Jiachen Yao, Chang Su, Hang Su, Ziao Wang, Fanzhi Lu, Zeyu Xia, Yichi Zhang, Songming Liu, Lu Lu, Jun Zhu, arXiv
An Expert's Guide to Training Physics-informed Neural Networks
Sifan Wang, Shyam Sankaran, Hanwen Wang, Paris Perdikaris, arXiv