(Must Read) Papers

Physics-informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations

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 Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

• Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations

• https://maziarraissi.github.io/PINNs/

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) 

Extended Physics-informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition based Deep Learning Framework for Nonlinear Partial Differential Equations

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

On the Eigenvector Bias of Fourier Feature Networks: From Regression to Solving Multi-scale PDEs with Physics-informed Neural Networks, 

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