Convolution-Based Model-Solving Method for Three-Dimensional, Unsteady, Partial Differential Equations

Data-driven deep learning of partial differential equations in modal space

(2020) Kailiang Wu et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Estimating the water characteristic curve for soil containing residual plastic film based on an improved pore-size distribution

(2020) Zhichao Wang et al.   GEODERMA

Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

(2020) Ameya D. Jagtap et al.   PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

ConvPDE-UQ: Convolutional neural networks with quantified uncertainty for heterogeneous elliptic partial differential equations on varied domains

(2019) Nick Winovich et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Identification of physical processes via combined data-driven and data-assimilation methods

(2019) Haibin Chang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Adaptive activation functions accelerate convergence in deep and physics-informed neural networks

(2019) Ameya D. Jagtap et al.   JOURNAL OF COMPUTATIONAL PHYSICS

PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network

(2019) Zichao Long et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Solving Partial Differential Equation Based on Bernstein Neural Network and Extreme Learning Machine Algorithm

(2018) Hongli Sun et al.   NEURAL PROCESSING LETTERS

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

Image Restoration: Wavelet Frame Shrinkage, Nonlinear Evolution PDEs, and Beyond

(2017) Bin Dong et al.   MULTISCALE MODELING & SIMULATION

Data-driven discovery of partial differential equations

(2017) Samuel H. Rudy et al.   Science Advances

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

(2016) Steven L. Brunton et al.   PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA

Image restoration: Total variation, wavelet frames, and beyond

(2012) Jian-Feng Cai et al.   JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY

An exponential high-order compact ADI method for 3D unsteady convection-diffusion problems

(2012) Yongbin Ge et al.   NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Complex variable boundary element-free method for two-dimensional elastodynamic problems

(2009) K.M. Liew et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING