About

I work on generative modeling for science — building learned priors that help us solve inverse problems governed by partial differential equations, where measurements are scarce and the physics is non-trivial.

I am an incoming Ph.D. student in Statistics & Data Science at Yale University, joining the Lu Group under Prof. Lu Lu. My recent work pairs diffusion-based priors with PDE-constrained optimization for full-waveform inversion, but I’m broadly interested in how generative models change the way we do inference in scientific computing.

Outside of research, my favourite distraction is my cat, 水墨 — a seal-point Siamese who lives back home in China with my family. Yale is too far for a cat, so I have to settle for her photos and my parents’ reports from the field. I don’t have many other hobbies, and I’ve made peace with that.

  • diffusion models
  • inverse problems
  • scientific machine learning
  • full waveform inversion
  • PDE-constrained optimization
  • regularization by denoising

Publications

3 papers
  1. RED-DiffEq — diffusion prior revealing a subsurface velocity model

    RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion

    S. Shan, M. Zhu, Y. Lin, L. Lu

    Communications Physics 2026 · Nature Portfolio

    Blog explainer → Paper Code BibTeX
  2. FunDiff

    FunDiff: diffusion models over function spaces for physics-informed generative modeling

    S. Wang, Z. Dou, S. Shan, et al.

    Nature Communications 2026 · Nature Portfolio

    Paper
  3. PiRD

    PiRD: Physics-informed Residual Diffusion for Flow Field Reconstruction

    S. Shan, P. Wang, S. Chen, J. Liu, C. Xu, S. Cai

    Acta Mechanica Sinica 2025 · Springer Nature

    Paper arXiv

Blog & paper explainers

2 posts
  • 2026 · May

    my cat

    A seal-point Siamese named 水墨, who lives back home in China — and an interactive Siamese you can pet without the long flight.

    3 min read
  • 2026 · May

    Teaching a diffusion model to invert the wave equation

    A walkthrough of RED-DiffEq: how a denoising diffusion prior, trained once on a single dataset, can regularize seismic full-waveform inversion across very different geological domains.

    10 min read