Xinliang Liu

About

I am an Associate Professor at Ocean University of China. My research develops mathematical and computational tools for scientific machine learning, with an emphasis on neural operators, neural-network theory, and efficient solvers for multiscale partial differential equations.

Previously, I was a Postdoctoral Fellow in Computer, Electrical and Mathematical Science and Engineering at King Abdullah University of Science and Technology (KAUST) (2022–2025), working with Prof. Jinchao Xu. I received my Ph.D. in Applied Mathematics from Shanghai Jiao Tong University in 2021 under the supervision of Prof. Lei Zhang, and was a visiting scholar at Caltech with Prof. Houman Owhadi in 2019–2020.

News

• 2026: I am serving as an Area Chair for ICLR 2026 and NeurIPS 2026.
• September 2025: I joined Ocean University of China as an Associate Professor.
• April–May 2025: I gave an invited talk at 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

I develop AI-driven numerical methods for scientific computing, especially for multiscale problems and partial differential equations. My work connects approximation theory and numerical analysis with modern machine learning.

• Neural-network theory, kernels, and approximation
• Operator learning and AI for PDEs
• Multiscale, multigrid, and numerical homogenization methods
• Graph learning and scientific machine learning

My work has appeared in Journal of Computational Physics, SIAM Multiscale Modeling & Simulation, Applied and Computational Harmonic Analysis, NeurIPS, ICLR, and LoG.

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 Accepted for publication in Mathematics of Computation arXiv:2505.00351

Published Papers

1. Self-composing neural operators for high-frequency and multiscale PDE surrogates J He, X Liu, J Xu Journal of Computational Physics, 2026, 115189 DOI: 10.1016/j.jcp.2026.115189
2. A MGNO method for multiphase flow in porous media X Liu, X Yang, CS Zhang, L Zhang, L Zhao Annual Meeting Conference, 2024
3. Framelet message passing X Liu, B Zhou, C Zhang, YG Wang Applied and Computational Harmonic Analysis 78, 101773, 2025 arXiv:2302.14806
4. Dilated convolution neural operator for multiscale partial differential equations B Xu, X Liu^#, L Zhang Journal of Computational and Applied Mathematics 461, 116408, 2025
5. 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
6. Mitigating spectral bias for the multiscale operator learning X Liu, B Xu, S Cao, L Zhang Journal of Computational Physics 506, 112944, 2024
7. MgNO: Efficient Parameterization of Linear Operators via Multigrid J He, X Liu^#, J Xu ICLR 2024
8. 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)
9. 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
10. Iterated numerical homogenization for multiscale elliptic equations with monotone nonlinearity X Liu, E Chung, L Zhang Multiscale Modeling & Simulation 19 (4), 1601-1632, 2021
11. 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
12. 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

Appointments & Education

• Ocean University of China, Associate Professor (September 2025–present)
• King Abdullah University of Science and Technology (KAUST), Postdoctoral Fellow, Computer, Electrical and Mathematical Science and Engineering (February 2022–June 2025)
  Supervisor: 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 Mathematics (2008 - 2012)

Service & Recognition

• Area Chair: International Conference on Learning Representations (ICLR) and Conference on Neural Information Processing Systems (NeurIPS), 2026.
• Research grants: National Natural Science Foundation of China Young Scientists Fund (PI, 2025–2027); Pearl River Talent Program, Young Top-notch Talent.
• Recognition: First Place, AI4S Cup Competition (2024); ICLR Spotlight Paper (2023).
• 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.