My full list of publications/preprints can be found at this Google Scholar page or ResearchGate site.
My full list of publications/preprints can be found at this Google Scholar page or ResearchGate site.
Representative Recent Works (in each field):
(* Corresponding author. Numerical and Mathematical analysis papers follow alphabetical order if I am not the first author.)
Scientific Machine Learning for PDEs:
Qiao Zhuang, Taorui Wang, Rita Wanjiku, Majid Bani-Yaghoub, and Zhongqiang Zhang. Two-scale Neural Networks for Singularly Perturbed Dynamical Systems with Multiple Parameters, Results in Applied Mathematics, 32: 100766 (2026). [Journal] [arXiv]
Mohammed Alanazi, Majid Bani-Yaghoub and Qiao Zhuang. Sparse Discovery of Distributed-Delay PDEs with Bayesian Optimization, Submitted (2026).
Changhong Mou, Yeyu Zhang, Xuewen Zhu and Qiao Zhuang*. PAS-Net: Physics-informed Adaptive Scale Deep Operator Network, Submitted (2025). [arXiv]
Qiao Zhuang, Chris Ziyi Yao, Zhongqiang Zhang and George Em Karniadakis. Two-scale Neural Networks for Partial Differential Equations with Small Parameters, Communications in Computational Physics, 38(3): 603-629, (2025). [Journal] [arXiv]
AI4Math and AI-Assisted Mathematical Analysis
Chenyang An, Yu Wang, Qihao Ye, Zhongqiang Zhang, and Qiao Zhuang*. Carleman Estimates for Wave Equations on the Half-Line: AI-Assisted Weights and Applications, Submitted (2026). [arXiv]
Machine Learning for Science:
C. Liu, Y. Liu, T. Wang, Q. Zhuang, J. C. Liang, W. Yang, R. Xu, Q. Wang, D. Liu, and C. Han. On-the-Fly VLA Adaptation via Test-Time Reinforcement Learning, Accepted by ACL 2026 Main Conference (2026). [arXiv] [ACL Anthology]
( This work was recently mentioned by Profs. Emmanuel Dupoux, Yann LeCun, and Jitendra Malik, in the “The Path Forward” section of their work, “Why AI Systems Don’t Learn and What to Do About It: Lessons on Autonomous Learning from Cognitive Science.” It was also cited by Prof. Fei-Fei Li and the co-authors in their work "RoboTTT: Context Scaling for Robot Policies.")
Qiao Zhuang, Changhong Mou, Bowen Liu, Gregory King, and Mei Rosemary Fu. REINA: A Recognize-Then-Infer Wearable-to-App AI Framework for Breast Cancer Rehabilitation, Submitted (2026). [medRxiv]
Radial Basis Function Methods:
Qiao Zhuang*, Yanzhi Zhang, and Zhongqiang Zhang. Meshless Collocation Methods for Time-dependent Nonlocal Problems Based on Radial Basis Functions, Electronic Research Archive, 34(2): 1124-1156, (2026). [Journal]
Qiao Zhuang, Alfa Heryudono, Fanhai Zeng and Zhongqiang Zhang. Collocation Methods for Integral Fractional Laplacian and Fractional PDEs Based on Radial Basis Functions. Applied Mathematics and Computation, 469:128548, (2024). [Journal] [SSRN]
Immersed Finite Element Methods for Interface Problems:
Qiao Zhuang*, Zhongqiang Zhang, Marcus Sarkis and Tao Lin. Higher Degree Rectangular Immersed Finite Elements Discontinuous Galerkin Methods for Elliptic Interface Problems. Journal of Computational and Applied Mathematics, 476: 117126 (2025). [Journal]
Jin Wang, Xu Zhang and Qiao Zhuang*. An Immersed Crouzeix-Raviart Finite Element Method for Navier-Stokes Interface Problems With Moving Interfaces. International Journal of Numerical Analysis and Modeling, 19(4):563-586, (2022) . [Journal]
Slimane Adjerid, Tao Lin and Qiao Zhuang*. Error estimates for an immersed finite element method for second order hyperbolic equations in inhomogeneous media. Journal of Scientific Computing 84:35, (2020). [Journal]