no code implementations • 16 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.
no code implementations • 16 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.
no code implementations • 23 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.
no code implementations • 16 Oct 2023 • Juncai He, Xinliang Liu, Jinchao Xu
In this work, we propose a concise neural operator architecture for operator learning.
no code implementations • 28 Feb 2023 • Xinliang Liu, Bingxin Zhou, Chutian Zhang, Yu Guang Wang
Graph neural networks (GNNs) have achieved champion in wide applications.
no code implementations • 19 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).
1 code implementation • 11 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.
1 code implementation • 15 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.
no code implementations • 2 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