I am a 4th-year undergraduate in Computational Mathematics at Peking University. I am going to become a PhD in Applied Mathematics at Columbia University. My research lies at the intersection of high-dimensional PDEs, scientific computing, stochastic dynamics, and non-equilibrium Markov processes. I build theory-backed algorithms and scale them to high-dimensional experiments. Here is my CV.
📝 Publications
For a complete and up-to-date list, visit my Google Scholar profile.
🎖 Honors and Awards
(to be filled / updated)
📖 Education
- Sep 2022 - Jun 2026, Peking University (PKU), B.S. in Computational Mathematics
- Aug 2026 -, Columbia University, PhD. in Applied Mathematics
💬 Invited Talks
(to be updated when scheduled)
💻 Internships
(to be updated)
🔬 Research Experience
Sharp hypocoercive convergence estimates for nonequilibrium dynamics — Jul 2025 – Present
Supervisors: Prof. Jianfeng Lu (Duke), Prof. Bowen Li (CityU)
Designed a novel gapped-DMS method for sharp hypocoercive estimate of convergence rate. A preview on underdamped Langevin can be found here (arXiv). We are building a general nonequilibrium version that establish the square root and perturbation threshold explicitly, and potentially there would also be a time discrete version as well.
Simulation-Calibrated Algorithm for High-Dimensional PDEs (SCaSML) — Jun 2024 – Apr 2025
Supervisors: Prof. Yiping Lu (Northwestern), Dr. Yan Sun (Georgia Tech)
Proposed SCaSML, a simulation-calibrated pipeline correcting PINN bias via Multilevel Picard-style estimators with provably improved complexity scaling on 100d+ benchmarks. (arXiv)
Continuous-State Contextual Bandit with Pessimism Regularization — Aug 2024 – Nov 2025
Supervisor: Prof. Ying Jin (Harvard)
Extended pessimism regularization to continuous state/action spaces with function approximation, proving regret guarantees without uniform-overlap assumptions.
Flow-Calibrated Stochastic Control for Transition Path Sampling — Feb 2024 – Jun 2024
Supervisors: Prof. Yiping Lu (Courant), Dr. Dinghuai Zhang (Mila)
Reformulated transition-path sampling as stochastic optimal control and developed continuous SAC and GFlowNet variants guided by flow-based calibration.
Unbiased Square-Root Convergent Estimation for High-Dimensional Semilinear Parabolic PDEs — Sep 2023 – Feb 2024
Supervisor: Prof. Yiping Lu (Courant)
Developed an unbiased estimator combining Multilevel Picard iteration with randomized MLMC, establishing unbiasedness and variance bounds.
📚 Academic Activities
- Graduate course: Combinatorics (Score: 92), Prof. Chunwei Song — Spring 2023
- Graduate course: Statistical Learning (Score: 93), Prof. Kedian Mou — Fall 2023
- Graduate course: High Dimensional Probability, Prof. Zhihua Zhang — Fall 2024
- Graduate course: Optimization Methods, Prof. Zaiwen Wen — Fall 2024
- Graduate course: Applied Stochastic Analysis, Prof. Tiejun Li — Fall 2024
- Seminars: Blowup in fluid equations; Stochastic optimal control (organizer: Dr. Xinhan Duan); LLM & Scientific Computing (Prof. Zaiwen Wen)
- Summer school: Beauty of Theoretical Computer Science (NJU) — Summer 2024
🌐 Social Activities
- Academic & Innovation Department, SMS Student Union — Spring 2023
- English Debate Club — Summer 2024
💻 Skills / Hobbies
- Programming Languages: Python, MATLAB, \LaTeX, Markdown
- Numerical & Scientific Computing Tools: PyTorch, TensorFlow, JAX, NumPy, DeepXDE, WandB
- Numerical / Math Techniques: Multilevel Picard, MLMC, Krylov solvers, reduced-order modelling, hypocoercivity, concentration inequalities, optimal transport
- Hobbies: Animation, program design
- Languages: Mandarin (native), English (fluent)