Search Results for author: Xinliang Liu

Found 9 papers, 2 papers with code

Dilated convolution neural operator for multiscale partial differential equations

no code implementations16 Jul 2024 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.

Operator learning

A MgNO Method for Multiphase Flow in Porous Media

no code implementations16 Jun 2024 Xinliang Liu, Xia Yang, Chen-Song Zhang, Lian Zhang, Li Zhao

This research investigates the application of Multigrid Neural Operator (MgNO), a neural operator architecture inspired by multigrid methods, in the simulation for multiphase flow within porous media.

Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partials Differential Equations

no code implementations23 May 2024 Wenrui Hao, Xinliang Liu, Yahong Yang

Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering.

MgNO: Efficient Parameterization of Linear Operators via Multigrid

no code implementations16 Oct 2023 Juncai He, Xinliang Liu, Jinchao Xu

In this work, we propose a concise neural operator architecture for operator learning.

Operator learning

Framelet Message Passing

no code implementations28 Feb 2023 Xinliang Liu, Bingxin Zhou, Chutian Zhang, Yu Guang Wang

Graph neural networks (GNNs) have achieved champion in wide applications.

Node Classification

Mitigating spectral bias for the multiscale operator learning

no code implementations19 Oct 2022 Xinliang Liu, Bo Xu, Shuhao Cao, Lei Zhang

Neural operators have emerged as a powerful tool for learning the mapping between infinite-dimensional parameter and solution spaces of partial differential equations (PDEs).

Operator learning

ACMP: Allen-Cahn Message Passing for Graph Neural Networks with Particle Phase Transition

1 code implementation11 Jun 2022 Yuelin Wang, Kai Yi, Xinliang Liu, Yu Guang Wang, Shi Jin

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.

Node Classification

Spectral Transform Forms Scalable Transformer

1 code implementation15 Nov 2021 Bingxin Zhou, Xinliang Liu, Yuehua Liu, Yunying Huang, Pietro Liò, Yuguang Wang

The architecture is assembled with a few simple effective computational blocks that constitute randomized SVD, MLP, and graph Framelet convolution.

Graph Learning Philosophy

Generalized Rough Polyharmonic Splines for Multiscale PDEs with Rough Coefficients

no code implementations2 Mar 2021 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 coefficients.

Numerical Analysis Numerical Analysis

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