About¶

I am an Incoming Ph.D. student at the National University of Singapore (NUS) and an undergraduate student in Mathematics and Applied Mathematics at Zhejiang University. My current interests lie in structure-preserving operator learning, scientific machine learning, numerical analysis for partial differential equations, and computational fluid dynamics.

News¶

• 2025 Received the Chu Kochen Scholarship at Zhejiang University.
• 2025 Continued work on structure-preserving operator learning and scientific machine learning.
• 2025 Prepared manuscripts on model-error learning and neural operators for convection-diffusion regimes.
• Upcoming Will join the National University of Singapore (NUS) as a Ph.D. student.

Research Interests¶

• Structure-Preserving Operator Learning
• Scientific Machine Learning (SciML)
• Numerical Analysis for PDEs

Publications & Manuscripts¶

• Learning missing physics from legacy simulators with alternating neural integrators
  Hao Wang, Qinghe Wang, Caiyou Yuan, and Kailiang Wu. Manuscript accepted, 2026.

Education¶

National University of Singapore (NUS)
Incoming Ph.D. student

Zhejiang University
Undergraduate student in Mathematics and Applied Mathematics, 2022.09-Present

Research Experience¶

Research Intern, Georgia Institute of Technology
Supervisor: Prof. Qi Tang, 2025.12-2026.04

• Collaborated weekly on structure-preserving operator learning for problems in plasma and fusion modeling.
• Designed a solution embedding a semi-Lagrangian discretization into a Fourier Neural Operator to bridge advection and diffusion-dominated regimes.
• Developed and validated a single model for both sharp shock structures and smooth convection-diffusion behavior.

Research Intern, Southern University of Science and Technology
Supervisor: Prof. Kailiang Wu, 2025.07-2025.08

• Translated an operator-splitting and machine-learning correction framework into a computational model for model-reality gaps.
• Studied stability and approximation properties of the proposed operator-learning framework.
• Implemented and benchmarked the framework on Navier-Stokes, FitzHugh-Nagumo, and one-dimensional compressible Euler systems.

Research Projects¶

Zhejiang Province SRTP Project: Application and Optimization of Classical Computational Methods and Machine Learning Techniques in Flow Field Simulation
Supervisor: Prof. Heyu Wang, 2024.03-2025.05

• Worked with a finite-element program for solving the Navier-Stokes equations and gained hands-on experience in computational fluid dynamics.
• Explored the integration of classical computational methods with machine learning to improve simulation accuracy and reduce computational cost.
• Investigated optimization techniques and loss functions for Physics-Informed Neural Network models.

Honors & Awards¶

• Chu Kochen Scholarship, Zhejiang University, 2025
• National Scholarship, Ministry of Education of China, 2023, 2024, 2025
• Bronze Award, Shing-Tung Yau College Student Mathematics Competition, Applied and Computational Mathematics category, 2025
• First-Class Scholarship, Zhejiang University, 2023, 2024, 2025
• Finalist, Mathematical Contest in Modeling (MCM/ICM), 2024

Seminars & Reading Groups¶

• Fourier Analysis Reading Group, Zhejiang University, 2024.07
  Studied Fourier Analysis: An Introduction by E. M. Stein and R. Shakarchi.

• Finite Element Methods Reading Group, Zhejiang University, 2024
  Studied The Mathematical Theory of Finite Element Methods by S. C. Brenner and L. R. Scott.

• Spectral Methods Group, Zhejiang University, 2025
  Studied Spectral Methods: Algorithms, Analysis and Applications by Jie Shen, Tao Tang, and Li-Lian Wang.

Leadership & Initiatives¶

Founder and Maintainer, Rhythm of Mathematics Resource Sharing Website
2024.06-Present

• Developed and launched a resource-sharing platform for Zhejiang University students.
• Collaborated with the Zhejiang University Youth League Committee to promote and support the platform.
• Curated study materials, notes, and peer advice for mathematics courses.

Technical Skills¶

• Machine Learning: PyTorch; neural-network setup, training, and fine-tuning; CNNs; PINNs.
• Operating Systems: Linux command-line tools for simulation setup, code execution, and data processing.