On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks

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

(2020) Maziar Raissi et al.   SCIENCE

Physics-Informed Neural Networks for Cardiac Activation Mapping

(2020) Francisco Sahli Costabal et al.   Frontiers in Physics

Physics-informed neural networks for inverse problems in nano-optics and metamaterials

(2020) Yuyao Chen et al.   OPTICS EXPRESS

Array programming with NumPy

(2020) Charles R. Harris et al.   NATURE

Systems biology informed deep learning for inferring parameters and hidden dynamics

(2020) Alireza Yazdani et al.   PLoS Computational Biology

Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data

(2019) Yinhao Zhu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Adversarial uncertainty quantification in physics-informed neural networks

(2019) Yibo Yang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data

(2019) Luning Sun et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks

(2019) Georgios Kissas et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks

(2019) Sharmila Karumuri et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Solving high-dimensional partial differential equations using deep learning

(2018) Jiequn Han et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

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

(2018) M. Raissi et al.   JOURNAL OF COMPUTATIONAL PHYSICS