540 citations · 908 across the 23 of their papers we have counts for
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Laplace-fPINNs: Laplace-based fractional physics-informed neural networks for solving forward and inverse problems of subdiffusion
Xiong-Bin Yan, Zhi-Qin John Xu, Zheng Ma
The use of Physics-informed neural networks (PINNs) has shown promise in solving forward and inverse problems of fractional diffusion equations. However, due to the fact that autom…
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…
Asymptotic-Preserving Neural Networks for Multiscale Time-Dependent Linear Transport Equations
Shi Jin, Zheng Ma, Keke Wu
In this paper we develop a neural network for the numerical simulation of time-dependent linear transport equations with diffusive scaling and uncertainties. The goal of the networ…
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…