4 papers
Multi-stage neural operator learning with application for convolutions
Zhiping Mao, Zhenye Wen, Yong Zhang +1
Convolution integrals widely exist in applications, and to enable fast and accurate computations, this paper introduces two general multi-stage neural operator learning frameworks.…
Error Bound Analysis of Physics-Informed Neural Networks-Driven T2 Quantification in Cardiac Magnetic Resonance Imaging
Mengxue Zhang, Qingrui Cai, Yinyin Chen +13
Physics-Informed Neural Networks (PINN) are emerging as a promising approach for quantitative parameter estimation of Magnetic Resonance Imaging (MRI). While existing deep learning…
Deep collocation method: A framework for solving PDEs using neural networks with error control
Mingxing Weng, Zhiping Mao, Jie Shen
Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-sh…
A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems
Xiangnan Yu, Hao Xu, Zhiping Mao +4
In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order…