Related papers: On Bayesian Consistency for Flows Observed Through…
We propose a generative multivariate posterior sampler via flow matching. It offers a simple training objective, and does not require access to likelihood evaluation. The method learns a dynamic, block-triangular velocity field in the joint…
We study passive scalar mixing by parallel shear flows in the presence of weak molecular diffusion. We recover the sharp uniform-in-diffusivity mixing rate for shear flows with finitely many critical points, recently proven in [1]. Our…
We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime based on one-step generative transport. Building on the Mean Flows, we learn a fully conditional amortized sampler with a neural-operator…
We propose a fast, stable, and direct analytic method to detect underwater channel topography from surface wave measurements, based on one-dimensional shallow water equations. The technique requires knowledge of the free surface and its…
In 1959, Batchelor predicted that the stationary statistics of passive scalars advected in fluids with small diffusivity $\kappa$ should display a $|k|^{-1}$ power spectrum along an inertial range contained in the viscous-convective range…
The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a MAP estimator. The MAP estimator essentially coincides with the (regularised) variational solution to the inverse…
The problem of locating an odor source in turbulent flows is central to key applications such as environmental monitoring and disaster response. We address this challenge by designing an algorithm based on Bayesian inference, which uses…
We study nonparametric Bayesian models for reversible multi-dimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift…
The structure of boundary currents formed from intermediately dense water introduced into a rotating, stably stratified, two-layer environment is investigated in a series of laboratory experiments, performed for Froude numbers ranging from…
This paper presents a method for finding a sparse representation of Barron functions. Specifically, given an $L^2$ function $f$, the inverse scale space flow is used to find a sparse measure $\mu$ minimising the $L^2$ loss between the…
In this article, we study the regularity theory for two linear equations that are important in fluid dynamics: the passive scalar equation for (time-varying) shear flows close to Couette in $\mathbb T \times [-1,1]$ with vanishing…
Flow matching is a recent state-of-the-art framework for generative modeling based on ordinary differential equations (ODEs). While closely related to diffusion models, it provides a more general perspective on generative modeling. Although…
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
Using high-fidelity numerical simulations based on a lattice Boltzmann framework, the advection-enhanced transport of a passive scalar from a prolate spheroid in simple shear flow has been thoroughly investigated across various parameters,…
This contribution investigates an original stochastic approach for the emergence of stop-and-go waves in traffic flow, a collective phenomenon with significant safety and environmental implications. Using a stable nonlinear car-following…
We study the inverse problem of recovering a spatially dependent variable order in a time-fractional diffusion model from the boundary flux measurement generated by a single boundary excitation. It arises in the identification of…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
We consider the statistical nonlinear inverse problem of recovering the absorption term $f>0$ in the heat equation $$ \partial_tu-\frac{1}{2}\Delta u+fu=0 \quad \text{on $\mathcal{O}\times(0,\textbf{T})$}\quad u = g \quad \text{on…
A fundamental aspect of turbulence theory is related to the identification of realizable phase-space statistical descriptions able to reproduce in some suitable sense the stochastic fluid equations of a turbulent fluid. In particular, a…
We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…