70 citations · 164 across the 35 of their papers we have counts for
5 papers · 1 filter
On understanding and overcoming spectral biases of deep neural network learning methods for solving PDEs
Zhi-Qin John Xu, Lulu Zhang, Wei Cai
In this review, we survey the latest approaches and techniques developed to overcome the spectral bias towards low frequency of deep neural network learning methods in learning mul…
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…
An Unsupervised Deep Learning Approach for the Wave Equation Inverse Problem
Xiong-Bin Yan, Keke Wu, Zhi-Qin John Xu +1
Full-waveform inversion (FWI) is a powerful geophysical imaging technique that infers high-resolution subsurface physical parameters by solving a non-convex optimization problem. H…
Bayesian Inversion with Neural Operator (BINO) for Modeling Subdiffusion: Forward and Inverse Problems
Xiong-bin Yan, Zhi-Qin John Xu, Zheng Ma
Fractional diffusion equations have been an effective tool for modeling anomalous diffusion in complicated systems. However, traditional numerical methods require expensive computa…
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…