Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems

Efficient training of physics‐informed neural networks via importance sampling

(2021) Mohammad Amin Nabian et al.   COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING

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

Systematic Construction of Neural Forms for Solving Partial Differential Equations Inside Rectangular Domains, Subject to Initial, Boundary and Interface Conditions

(2020) P. L. Lagari et al.   International Journal on Artificial Intelligence Tools

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

(2020) Yuyao Chen et al.   OPTICS EXPRESS

PPINN: Parareal physics-informed neural network for time-dependent PDEs

(2020) Xuhui Meng et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Systems biology informed deep learning for inferring parameters and hidden dynamics

(2020) Alireza Yazdani et al.   PLoS Computational Biology

Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems

(2019) Dongkun Zhang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Physics Informed Extreme Learning Machine (PIELM)–A rapid method for the numerical solution of partial differential equations

(2019) Vikas Dwivedi et al.   NEUROCOMPUTING

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

Unifying Adversarial Training Algorithms with Data Gradient Regularization

(2017) Alexander G. Ororbia II et al.   NEURAL COMPUTATION

Artificial Neural Network Method for Solution of Boundary Value Problems With Exact Satisfaction of Arbitrary Boundary Conditions

(2009) K.S. McFall et al.   IEEE TRANSACTIONS ON NEURAL NETWORKS

Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques

(2009) R. Shekari Beidokhti et al.   JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS