Xinliang Liu

About Me

I am currently a Postdoctoral Fellow at the Extreme Computing Research Center (ECRC) at King Abdullah University of Science and Technology (KAUST), working with Prof. Jinchao Xu since 2022.

I received my Ph.D. in Applied Mathematics from Shanghai Jiao Tong University in 2021, supervised by Prof. Lei Zhang. During my Ph.D., I was fortunate to spend time as a Visiting Scholar at the California Institute of Technology (Caltech), hosted by Prof. Houman Owhadi (2019-2020). Prior to my doctoral studies, I obtained my Master of Science in Applied Mathematics (2017) from Shanghai Jiao Tong University and my Bachelor of Science in Information and Computing Science (2012) from Ningbo University.

News

• April 27 - May 2, 2025: I will attend the Oberwolfach Workshop on Computational Multiscale Methods. [MFO]
• June 2024: Honored to receive First Prize in the "AI for Science" competition hosted by the DeepModeling community on the Bohrium platform. Our model, MgNO, was a collaborative effort with Juncai He and Bo Xu (SJTU). [Competition Details]

Research Interests

My research focuses on developing efficient numerical methods and machine learning models for scientific computing problems, particularly those involving multiscale phenomena or described by partial differential equations (PDEs). Key areas include:

• Numerical Homogenization & Multiscale Methods
• Multigrid and Domain Decomposition Methods
• Graph Neural Networks (GNNs) for Scientific Computing
• Neural Operators and AI for PDEs
• Kernel Methods

My work has been published in journals and conferences such as the Journal of Computational Physics (JCP), SIAM Multiscale Modeling & Simulation (MMS), Applied and Computational Harmonic Analysis, NeurIPS, and ICLR.

Publications

Preprints

1. Diff-ANO: Towards Fast High-Resolution Ultrasound Computed Tomography via Conditional Consistency Models and Adjoint Neural Operators X Cao, Q Ding, X Liu, L Zhang, X Zhang arXiv preprint arXiv:2507.16344, 2025 arXiv:2507.16344
2. OpenBreastUS: Benchmarking Neural Operators for Wave Imaging Using Breast Ultrasound Computed Tomography Z Zeng, Y Zheng, H Hu, Z Dong, Y Zheng, X Liu, J Wang, Z Shi, L Zhang arXiv preprint arXiv:2507.15035, 2025 arXiv:2507.15035
3. Advanced long-term earth system forecasting by learning the small-scale nature H Wu, Y Gao, R Shu, K Wang, R Gou, C Wu, X Liu, J He, S Cao, J Xu arXiv preprint arXiv:2505.19432, 2025 arXiv:2505.19432
4. Integral Representations of Sobolev Spaces via ReLU $^k$ Activation Function and Optimal Error Estimates for Linearized Networks X Liu, T Mao, J Xu arXiv preprint arXiv:2505.00351, 2025 arXiv:2505.00351

Published Papers

1. A MGNO method for multiphase flow in porous media X Liu, X Yang, CS Zhang, L Zhang, L Zhao Annual Meeting Conference, 2024
2. Framelet message passing X Liu, B Zhou, C Zhang, YG Wang Applied and Computational Harmonic Analysis 78, 101773, 2025 arXiv:2302.14806
3. Dilated convolution neural operator for multiscale partial differential equations B Xu, X Liu^#, L Zhang Journal of Computational and Applied Mathematics 461, 116408, 2025
4. Newton informed neural operator for solving nonlinear partial differential equations W Hao, X Liu, Y Yang Advances in Neural Information Processing Systems 37 (NeurIPS), 120832-120860, 2024
5. Mitigating spectral bias for the multiscale operator learning X Liu, B Xu, S Cao, L Zhang Journal of Computational Physics 506, 112944, 2024
6. MgNO: Efficient Parameterization of Linear Operators via Multigrid J He, X Liu^#, J Xu ICLR 2024
7. ACMP: Allen-Cahn Message Passing for Graph Neural Networks with Particle Phase Transition Y Wang, K Yi, X Liu, YG Wang, S Jin ICLR 2023 (Spotlight)
8. Well-conditioned spectral transforms for dynamic graph representation B Zhou, X Liu, Y Liu, Y Huang, P Lio, YG Wang Learning on Graphs Conference, 12: 1-12: 19, 2022
9. Iterated numerical homogenization for multiscale elliptic equations with monotone nonlinearity X Liu, E Chung, L Zhang Multiscale Modeling & Simulation 19 (4), 1601-1632, 2021
10. Generalized rough polyharmonic splines for multiscale pdes with rough coefficients X Liu, L Zhang, S Zhu Numer. Math. Theor. Meth. Appl. 14 (4), 862-892., 2021
11. Optimal control for multiscale equations with rough coefficients Y Chen, X Liu, J Zeng, L Zhang Journal of Computational Mathematics 41 (5), 842-866, 2021

Education

• King Abdullah University of Science and Technology (KAUST), Postdoc (2022 - Present)
  Advisor: Prof. Jinchao Xu
• Shanghai Jiao Tong University, Ph.D. in Applied Mathematics (2017 - 2021)
  Advisor: Prof. Lei Zhang
• California Institute of Technology (Caltech), Visiting Scholar (2019 - 2020)
  Host: Prof. Houman Owhadi
• Shanghai Jiao Tong University, Master of Science in Applied Mathematics (2014 - 2017)
• Ningbo University, Bachelor of Science in Information and Computing Science (2008 - 2012)

Professional Activities

• Co-organizer: Special Session on Analysis, Algorithms, and Applications of Neural Networks (with Juncai He and Jinchao Xu).
  The 14th AIMS Conference on Dynamical Systems, Differential Equations and Applications (AIMS 2024), Abu Dhabi, UAE, December 15-19, 2024.
• Co-organizer: Minisymposium on Multigrid and Multilayer Methods (with Juncai He and Jinchao Xu).
  International Multigrid Conference (IMG2022), Lugano, Switzerland, August 22-26, 2022.