24 citations · 27 across the 15 of their papers we have counts for
7 papers · 1 filter
A clever neural network in solving inverse problems of Schrödinger equation
Yiran Wang
In this work, we solve inverse problems of nonlinear Schrödinger equations that can be formulated as a learning process of a special convolutional neural network. Instead of attemp…
Gauss Newton method for solving variational problems of PDEs with neural network discretizaitons
Wenrui Hao, Qingguo Hong, Xianlin Jin
The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a pow…
A conservative multiscale method for stochastic highly heterogeneous flow
Yiran Wang, Eric Chung, Shubin Fu
In this paper, we propose a local model reduction approach for subsurface flow problems in stochastic and highly heterogeneous media. To guarantee the mass conservation, we conside…
Inverse Problem of Nonlinear Schrödinger Equation as Learning of Convolutional Neural Network
Yiran Wang, Zhen Li
In this work, we use an explainable convolutional neural network (NLS-Net) to solve an inverse problem of the nonlinear Schrödinger equation, which is widely used in fiber-optic co…
Constraint energy minimization generalized multiscale finite element method in mixed formulation for parabolic equations
Yiran Wang, Eric Chung, Lina Zhao
In this paper, we develop the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) in mixed formulation applied to parabolic equations with hete…
Adaptive multiscale model reduction for nonlinear parabolic equations using GMsFEM
Yiran Wang, Eric Chung, Shubin Fu
In this paper, we propose a coupled Discrete Empirical Interpolation Method (DEIM) and Generalized Multiscale Finite element method (GMsFEM) to solve nonlinear parabolic equations…