Sampling

Main fields of application

Sampling turns probability distributions into computable random representatives. We study the dynamics and geometry behind sampling algorithms, especially in high-dimensional and learning-related settings.

Diffusions, deterministic measure transport and gradient flows provide complementary routes through probability space. We analyse their convergence, stability and large-deviation structure, and investigate metrics such as transport and Fisher–Rao geometries that guide efficient updates. Connections to neural PDE solvers and generative models lead to numerical methods that combine analytical guarantees with scalable computation. The aim is to understand when an algorithm explores reliably, which geometric structure accelerates it, and how microscopic stochastic dynamics produce effective sampling schemes.

Current directions

  • Diffusion and transport-based sampling
  • Fisher–Rao and optimal-transport geometry
  • Convergence and stability
  • Neural PDE solvers
  • Generative models and scalable algorithms

Related people

Related projects

Selected publications

  • Weak synchronisation for McKean–Vlasov SDEs

    Synchronisation by noise for McKean–Vlasov stochastic differential equations is investigated. A transfer principle is introduced by which synchronisation by noise and diagonal mixing can be transferred from an associated limiting frozen-diffusion SDE to a genuinely law-dependent McKean–Vlasov SDE. The usefulness…

  • The Advective Fisher-Rao Geometry of Deterministic Measure Transport

    A novel advective Fisher-Rao metric is introduced for optimization tasks on paths of probability measures governed by the continuity equation. This metric is shown to lead to optimal descent directions. It is then shown that this metric arises naturally from three different…

  • Ergodicity for SPDEs driven by divergence-free transport noise

    We study the ergodic behaviour of the McKean-Vlasov equations driven by common, divergence-free transport noise. In particular, we show that in dimension $d\geq 2$, if the noise is mixing and sufficiently strong it can enforce the uniqueness of invariant probability measures, even…