I am an assistant professor in the Machine Learning Department and the Department of Mathematical Sciences at CMU. I lead a small, focused team that studies the algorithmic foundations of generative models and their application to problems across artificial intelligence, science, and engineering.
Previously, I was a Courant Instructor at the Courant Institute of Mathematical Sciences working with Eric Vanden-Eijnden. I completed my PhD in applied mathematics at Harvard co-advised by Jean-Jacques Slotine and Chris Rycroft. A longer bio is here.
Research / Publications / Code / Teaching / Application Materials
Research Group
The aim of our group is to develop principled methods for generative modeling and to apply them to problems across core machine learning, science, and engineering. We are particularly interested in scientific challenges that are impossible with more traditional computational tools. Some current topics of interest include accelerated inference in flows and diffusions, inference-time guidance, and sampling from unnormalized measures.
PhD Students
Jerry Huang
Computer Science Department
Stephen Huan
Computer Science Department
co-advised with Andrej Risteski
Masters Students
Kartik Nair
Machine Learning Department
Sheel Shah
Machine Learning Department
Undergraduate Students
Ishin Shah
Department of Mathematical Sciences
co-advised with Max Simchowitz
Publications
Code
We are strong advocates for reproducible science and open-source software. We believe that they have been key drivers of the recent advances in AI research, and we make all our code publicly available to continue this tradition.
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jax-interpolants
A JAX implementation of the stochastic interpolant framework for generative modeling -
jax-edm2
A JAX implementation of NVIDIA's EDM2 U-Net architecture -
flow-maps (with Michael Albergo and Eric Vanden Eijnden)
A JAX implementation of the self-distillation framework for learning flow maps and consistency models -
model-free probability flows (with Eric Vanden Eijnden)
Code for model-free learning of probability flows in nonequilibrium dynamics -
structured diffusion (with Arthur Jacot and Stephen Tu)
Experiments verifying provable guarantees for when shallow diffusion networks can learn hidden structure -
flow map matching (with Michael Albergo and Eric Vanden Eijnden)
A JAX implementation of the flow map matching framework for learning flow maps and consistency models -
forecasting with interpolants (with Mengjian Hua, Yifan Chen, Mark Goldstein, Eric Vanden Eijnden, and Michael Albergo -- mostly written by the first three authors!)
An implementation of probabilistic forecasting with stochastic interpolants -
active probability flows (with Eric Vanden Eijnden)
Code for learning probability flows and entropy production rates in active matter -
stochastic interpolants (with Michael Albergo and Eric Vanden Eijnden)
An implementation of the unifying stochastic interpolant framework for flows and diffusions in generative modeling -
score-based transport modeling (with Eric Vanden Eijnden)
Code for constructing a probability flow solution of the Fokker-Planck equation -
spin glass evolutionary dynamics (with Yipei Guo, Chris Rycroft, and Ariel Amir)
High-resolution C++ simulation code to model Lenski's Long-Term Evolution Experiment, taking into account microscopic epistasis and clonal interference in microbial evolution -
shear transformation zone++ (with Chris Rycroft)
Three-dimensional MPI-based C++ code for parallel simulation of quasi-static deformation in elastoplastic solids -
real-space Hartree-Fock (with Amir Natan, note: only the Hartree-Fock implementation)
Parallelized Fortran code to efficiently compute the Hartree-Fock exchange via the use of projection operators onto occupied and virtual states
Teaching
I teach mathematically- and computationally-oriented courses in applied mathematics and machine learning. Below is a list of past, present, and future offerings.
Carnegie Mellon, Spring 2025: Methods of Optimization
Carnegie Mellon, Fall 2024: Introduction to PDEs: A Computational Approach
NYU Courant, Spring 2024: Honors Numerical Analysis
NYU Courant, Fall 2023: Linear and Nonlinear Optimization
NYU Courant, Spring 2023: Linear and Nonlinear Optimization
NYU Courant, Fall 2022: Numerical Analysis
NYU Courant, Spring 2022: Linear and Nonlinear Optimization
NYU Courant, Fall 2021: Numerical Analysis
Northwestern, Full Year 2014: Introduction to Computer Programming for Integrated Science