7 citations · 18 across the 9 of their papers we have counts for
9 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.…
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…
Framelet Message Passing
Xinliang Liu, Bingxin Zhou, Chutian Zhang +1
Graph neural networks (GNNs) have achieved champion in wide applications. Neural message passing is a typical key module for feature propagation by aggregating neighboring features…
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…
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…
Spectral Transform Forms Scalable Transformer
Bingxin Zhou, Xinliang Liu, Yuehua Liu +3
Many real-world relational systems, such as social networks and biological systems, contain dynamic interactions. When learning dynamic graph representation, it is essential to emp…
Generalized Rough Polyharmonic Splines for Multiscale PDEs with Rough Coefficients
Xinliang Liu, Lei Zhang, Shengxin Zhu
In this paper, we demonstrate the construction of generalized Rough Polyhamronic Splines (GRPS) within the Bayesian framework, in particular, for multiscale PDEs with rough coeffic…
Iterated numerical homogenization for multi-scale elliptic equations with monotone nonlinearity
Xinliang Liu, Eric Chung, Lei Zhang
Nonlinear multi-scale problems are ubiquitous in materials science and biology. Complicated interactions between nonlinearities and (nonseparable) multiple scales pose a major chal…
Optimal control for multiscale equations with rough coefficients
Yanping Chen, Jiaoyan Zeng, Xinliang Liu +1
This paper concerns the convex optimal control problem governed by multiscale elliptic equations with arbitrarily rough coefficients, which has important applications in…