Designing Dynamic Measure Transport for Sampling

Sampling from a target probability distribution is fundamental to modern computational science and machine learning. Sampling is the essence of Monte Carlo integration, enables uncertainty quantification in Bayesian inference, and underlies generative models that have the ability to synthesize convincing text, images, and far beyond. A powerful, emerging approach to sampling is dynamic measure transport (DMT): the idea is to design an ordinary or stochastic differential equation that evolves samples from a tractable reference distribution (e.g., a Gaussian) to the desired target distribution. DMT is state-of-the-art in generative modeling and underlies techniques such as diffusion models and flow-matching, but DMT pipelines for density-driven sampling tasks, as arising in computational chemistry and Bayesian inference, are significantly less developed. In this talk, I will discuss my work to make density-driven DMT a reality via: (1) development of new, gradient-free particle systems for Bayesian sampling, (2) principled design of DMT via PDE-constrained optimization, and (3) scalability through the exploitation of sparse conditional dependence structure. I will describe how these efforts will enable new DMT approaches to complex sampling problems--such as ensemble data assimilation, in which the prior is only known through samples---and sketch future work on stochastic inverse problems, in which an unknown distribution must be recovered from indirect measurements. Speaker Bio: Aimee Maurais will graduate from MIT with her PhD in Computational Science and Engineering in May 2026. In August 2026 she will join Cornell University as a NSF Mathematical Sciences Postdoctoral Research Fellow. Prior to beginning her graduate work, Aimee earned bachelor’s degrees in Mathematics and Computational Modeling & Data Analytics from Virginia Tech and spent 1.5 years on the technical staff at MIT Lincoln Laboratory. Find seminar details and upcoming talks: https://www.microsoft.com/en-us/research/event/microsoft-research-new-england-generative-modeling-sampling-seminar/