540 citations · 833 across the 33 of their papers we have counts for
4 papers · 1 filter
Solving multiscale dynamical systems by deep learning
Junjie Yao, Yuxiao Yi, Liangkai Hang +5
Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of s…
MOD-Net: A Machine Learning Approach via Model-Operator-Data Network for Solving PDEs
Lulu Zhang, Tao Luo, Yaoyu Zhang +3
In this paper, we propose a a machine learning approach via model-operator-data network (MOD-Net) for solving PDEs. A MOD-Net is driven by a model to solve PDEs based on operator r…
Fourier-domain Variational Formulation and Its Well-posedness for Supervised Learning
Tao Luo, Zheng Ma, Zhiwei Wang +2
A supervised learning problem is to find a function in a hypothesis function space given values on isolated data points. Inspired by the frequency principle in neural networks, we…
Implicit bias with Ritz-Galerkin method in understanding deep learning for solving PDEs
Jihong Wang, Zhi-Qin John Xu, Jiwei Zhang +1
This paper aims at studying the difference between Ritz-Galerkin (R-G) method and deep neural network (DNN) method in solving partial differential equations (PDEs) to better unders…