Title

Accelerated sampling from Boltzmann distributions with diffusion and flows models

Challenge

Sampling from complex energy landscapes (Boltzmann distributions) is a fundamental challenge in science and ML. Traditional methods like MCMC are often slow to converge, struggle at large scale, and ML-based solutions may lack guarantees of correctness.

Description

This project will explore the use of generative models, specifically normalizing flows and diffusion models, to accelerate high-fidelity sampling from complex Boltzmann distributions. The research will focus on developing and evaluating techniques to overcome the limitations of traditional MCMC methods, aiming for efficient sampling at scale while ensuring high precision. Students will apply these methods to challenging problems in computational chemistry and physics, such as sampling molecular conformations or spin-glass configurations, and benchmark their accuracy in estimating key statistical properties (e.g., moments, free energies).

Skills Required

Probabilistic modelling, MCMC, normalising flows, diffusion models

Skills to be Developed

Generative models, advanced sampling methods

Relevant Background Reading:

1. https://arxiv.org/abs/2506.16471
2. https://arxiv.org/abs/2201.13117
3. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.121601
4. Midgley, L.I., Stimper, V., Simm, G.N., Schölkopf, B. and Hernández-Lobato, J.M., 2022. Flow annealed importance sampling bootstrap. arXiv preprint arXiv:2208.01893.
5. Cabezas, A., Sharrock, L. and Nemeth, C., 2024. Markovian Flow Matching: Accelerating MCMC with Continuous Normalizing Flows. arXiv preprint arXiv:2405.14392.