Zexi Fan

Zexi Fan

Peking University

I am a 3rd year undergraduate majoring in computational mathematics at Peking University.

My research interests include scientific machine learning, diffusion models，high dimensional PDE solvers, and any other related topics in applied mathematics.

Here is my CV.

πŸ”₯ News

πŸ“ Publications

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Physics-Informed Inference-Time Scaling for Solving High-dimensional PDE via Simula- tion Calibrated Scientific Machine Learning (SCaSML)(Comming Soon)

First Author: Zexi Fan

Project(Comming Soon)

  • Working on that.

πŸŽ– Honors and Awards

πŸ“– Educations

  • Sep 2022 - Present, Peking University(PKU), B.S. in Computational Mathematics
    • Major GPA: 3.6/4.0
    • Selected Courses: Abstract Algebra(93), Machine Learning(93), Advanced Algebra 2(90)
    • Advanced Mathematical Skills: Stochastic Analysis & Control, Scientific Machine Learning, PDE
    • GRE: (164+169+4)/(170+170+6) (Aug 2023)

πŸ’¬ Invited Talks

πŸ’» Internships

πŸ”¬ Research Experience

  • Unbiased Square Root Convergent Estimation for High-Dimensional Semilinear Parabolic Heat Equation (Sep 2023 - Feb 2024)
    • Supervisors: Prof. Yiping Lu at NYU
    • Proposed an estimator using Multilevel Picard Iteration and randomized Multilevel Monte Carlo
    • Proved the unbiasedness and bounded variance of the estimator
  • Flow Calibrated RL for Transition Path Sampling (Feb 2024 - June 2024)(Slides,Research Note)
    • Supervisors: Prof. Yiping Lu and Dr. Dinghuai Zhang at NYU, Mila
    • Proposed an algorithm for sampling distribution-to-distribution transition paths under the SDE framework
    • Developed continuous versions of Soft Actor-Crictic and GFlowNet by stochastic analysis
    • Implemented numerical experiments to confirm its efficacy
  • Simulation-Calibrated Scientific Machine Learning (SCaSML) for Solving High-Dimensional Partial Differential Equations (June 2024 - Present)(Codebase for PINN,Codebase for Gaussian Kernel)
    • Supervisors: Prof. Yiping Lu and Dr. Yan Sun at Northwestern, Gatech
    • Developed simulation-based estimators to calibrate PINN error
    • Demonstrated SCaSML effectiveness through numerical experiments on multiple high dim PDEs
  • Continuous State Contextual Bandit with Pessimism Regularization (August 2024 - Present)
    • Supervisors: Prof. Ying Jin at Havard
    • Constructed an adaptation Pessimism Regularization for contextual bandit with continuous state space
    • Proved the suboptimality of the estimator does not require uniform overlapping assumption

πŸ“š Academic Activities

  • Graduate course: Combinatorics, Score: 92, taught by Prof. Chunwei Song (Spring 2023)
  • Graduate course: Machine learning, Score: 93, taught by Prof. Kedian Mou (Fall 2023)
  • Graduate course: Mathematical image processing, taught by Prof. Bin Dong (Fall 2023)
  • Graduate course: High Dimensional Probability, taught by Prof. Zhihua Zhang (Fall 2024)
  • Graduate course: Optimization Methods, taught by Prof. Zaiwen Wen (Fall 2024)
  • Graduate course: Applied Stochastic Analysis, taught by Prof. Tiejun Li (Fall 2024)
  • Seminar: Blowup in fluid equations, organized by Prof. Jiajun Tong & Prof. De Huang (Fall 2023)
  • Seminar: Stochastic optimal control, organized by Dr. Xinhan Duan (Spring 2024)
  • Seminar: Large Language Model and Scientific Computing, organized by Prof. Zaiwen Wen (Fall 2024)
  • Summer school: Beauty of theoretical computer science, organized by NJU CS Dept. (Summer 2024)

🌐 Social Activities

  • Academic & Innovation Department, SMS Student Union (Spring 2023)
  • English Debate Club (Summer 2024)

πŸ’» Skills/Hobbies

  • Programming Languages: Python, Matlab, Latex, Markdown
  • Machine Learning Tools: Pytorch, Tensorflow, Numpy, Jax, Wandb, DeepXDE
  • Hobbies: Animation and Program Designing
  • Languages: English and Chinese