4 papers
Diff-ANO: Towards Fast High-Resolution Ultrasound Computed Tomography via Conditional Consistency Models and Adjoint Neural Operators
Xiang Cao, Qiaoqiao Ding, Xinliang Liu +2
Ultrasound Computed Tomography (USCT) constitutes a nonlinear inverse problem with inherent ill-posedness that can benefit from regularization through diffusion generative priors.…
ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networks
Yuelin Wang, Kai Yi, Xinliang Liu +2
Neural message passing is a basic feature extraction unit for graph-structured data considering neighboring node features in network propagation from one layer to the next. We mode…
Dilated convolution neural operator for multiscale partial differential equations
Bo Xu, Xinliang Liu, Lei Zhang
This paper introduces a data-driven operator learning method for multiscale partial differential equations, with a particular emphasis on preserving high-frequency information. Dra…
Mitigating spectral bias for the multiscale operator learning
Xinliang Liu, Bo Xu, Shuhao Cao +1
Neural operators have emerged as a powerful tool for learning the mapping between infinite-dimensional parameter and solution spaces of partial differential equations (PDEs). In th…