PhD student in Statistics & Data Science at Yale University
Studying how foundation-model and agentic AI methods can discover symbolic partial differential equations from spatiotemporal data.
My current work is organized around one technical spine:
Symbolic PDE discovery with foundation models and agentic scientific-discovery systems.
| Direction | What I care about |
|---|---|
| FoundPDE | A generative, pre-trained data-to-symbol model that maps numerical solution data to symbolic PDE expressions. |
| Sparse-data symbolic discovery | Recovering governing equations from limited observations while keeping the discovered structure interpretable. |
| Compositional generalization | Extending beyond the pretraining distribution through few-shot adaptation and step-by-step recovery of composite equations. |
| PDEScientist | Agentic PDE discovery: an LLM-style system proposes equations, analyzes data, calls evaluators, fits coefficients, and refines hypotheses over turns. |
| Scientific evaluation | Building PDE-specific evaluation loops where targets, features, residuals, and coefficient optimization are controlled by the evaluator rather than the model. |
| Page | Why it is useful |
|---|---|
| Personal website | Clean overview of my research, projects, publications, and blog. |
| FoundPDE | Current foundation-model project for symbolic PDE discovery. |
| PDEScientist | Forward-looking agentic discovery project. |
| Reading Markowitz 1952 Through Geometry | Example of my research-note style: math, figures, references, and an interactive widget. |
- I like problems where machine learning has to produce scientific structure, not only low prediction error.
- I work with numerical PDE data, symbolic expressions, coefficient fitting, and evaluator-controlled validation loops.
- I am especially interested in systems that can propose hypotheses, test them against data, and revise them based on tool feedback.
- Yale University — PhD student, Statistics & Data Science
- University of Pennsylvania — PhD student, Applied Mathematics and Computational Science
- Duke University / Duke Kunshan University — BSc, Applied Mathematics
- Full website: decoderliu.github.io
- Publications: Google Scholar and ACL Anthology
- Professional profile: LinkedIn
- Contact: langchen.liu@yale.edu
Outside research, I play video games, with Overwatch 2 as a long-running favorite.