DWNN: Deep Wavelet Neural Network for Solving Partial Differential Equations

DeLISA: Deep learning based iteration scheme approximation for solving PDEs

(2021) Ying Li et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems

(2020) Ameya D. Jagtap et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Weak adversarial networks for high-dimensional partial differential equations

(2020) Yaohua Zang et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Deep learning-based method coupled with small sample learning for solving partial differential equations

(2020) Ying Li et al.   MULTIMEDIA TOOLS AND APPLICATIONS

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

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

A meshless symplectic method for two-dimensional nonlinear Schrödinger equations based on radial basis function approximation

(2019) Zhengjie Sun   ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS

A class of high-order compact difference schemes for solving the Burgers’ equations

(2019) Xiaojia Yang et al.   APPLIED MATHEMATICS AND COMPUTATION

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

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

Solving many-electron Schrödinger equation using deep neural networks

(2019) Jiequn Han et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Wind speed forecasting method based on deep learning strategy using empirical wavelet transform, long short term memory neural network and Elman neural network

(2018) Hui Liu et al.   ENERGY CONVERSION AND MANAGEMENT

Local discontinuous Galerkin methods with explicit Runge-Kutta time marching for nonlinear carburizing model

(2018) Chenghui Xia et al.   MATHEMATICAL METHODS IN THE APPLIED SCIENCES

DGM: A deep learning algorithm for solving partial differential equations

(2018) Justin Sirignano 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

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

Application of Legendre Neural Network for solving ordinary differential equations

(2016) Susmita Mall et al.   APPLIED SOFT COMPUTING

Single Layer Chebyshev Neural Network Model for Solving Elliptic Partial Differential Equations

(2016) Susmita Mall et al.   NEURAL PROCESSING LETTERS

Deep learning

(2015) Yann LeCun et al.   NATURE

Study on Optimal Design Based on Direct Coupling Between a FEM Simulation Model and L-BFGS-B Algorithm

(2013) M. S. Berkani et al.   IEEE TRANSACTIONS ON MAGNETICS

Modified wavelet neural network in function approximation and its application in prediction of time-series pollution data

(2011) Zarita Zainuddin et al.   APPLIED SOFT COMPUTING

Fluid Mechanics of Microrheology

(2010) Todd M. Squires et al.   Annual Review of Fluid Mechanics

A finite difference method for fractional partial differential equation

(2009) Yang Zhang   APPLIED MATHEMATICS AND COMPUTATION

A Wavelet-Laplace Variational Technique for Image Deconvolution and Inpainting

(2008) J.A. Dobrosotskaya et al.   IEEE TRANSACTIONS ON IMAGE PROCESSING

New travelling wave solutions to the Boussinesq and the Klein–Gordon equations

(2006) Abdul-Majid Wazwaz   Communications in Nonlinear Science and Numerical Simulation