VS-PINN: A fast and efficient training of physics-informed neural networks using variable-scaling methods for solving PDEs with stiff behavior

Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Maziar Raissi, Paris Perdikaris, George Em Karniadakis · Journal of Computational Physics · 2018 · 16.9K citations · Full text

Natural Sciences, Computer Science, Physics +16

DGM: A deep learning algorithm for solving partial differential equations

Justin Sirignano, Konstantinos Spiliopoulos · Journal of Computational Physics · 2018 · 2.1K citations · Full text

Natural Sciences, Computer Science, Mathematics +13

Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

Maziar Raissi, Alireza Yazdani, George Em Karniadakis · Science · 2020 · 2K citations · Full text

Computing, Computer Science, Physics +16

Solving high-dimensional partial differential equations using deep learning

Jiequn Han, Arnulf Jentzen, E Weinan · Proceedings of the National Academy of Sciences · 2018 · 1.7K citations · Full text

Computing, Computer Science, Physics +12

Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

Sifan Wang, Yujun Teng, Paris Perdikaris · SIAM Journal on Scientific Computing · 2021 · 1.6K citations

Natural Sciences, Computer Science, Physics +14