相关论文: Mixing Estimates for Passive Scalar Transport by $…
An algorithm to estimate motion from satellite imagery is presented. Dense displacement fields are computed from time-separated images of of significant convective activity using a Bayesian formulation of the motion estimation problem.…
We investigate the properties of discretizations of advection equations on non-cartesian grids and graphs in general. Advection equations discretized on non-cartesian grids have remained a long-standing challenge as the structure of the…
We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…
Integration against, and hence sampling from, high-dimensional probability distributions is of essential importance in many application areas and has been an active research area for decades. One approach that has drawn increasing attention…
We derive the form of reciprocal generalized radiative transfer (RGRT) that includes the Levermore-Pomraning attenuation law for paths leaving a deterministic origin. The resulting model describes linear transport within multi-dimensional…
We address the task of estimating multiple trajectories from unlabeled data. This problem arises in many settings, one could think of the construction of maps of transport networks from passive observation of travellers, or the…
In the field of optimal transport, two prominent subfields face each other: (i) unregularized optimal transport, "\`a-la-Kantorovich", which leads to extremely sparse plans but with algorithms that scale poorly, and (ii)…
We study the 2D Navier-Stokes equation with transport noise subject to periodic boundary conditions. Our main result is an error estimate for the time-discretisation showing a convergence rate of order (up to) 1/2. It holds with respect to…
We propose an alternative interpretation of Markovian transport models based on the well-mixedness condition, in terms of the properties of a random velocity field with second order structure functions scaling linearly in the space time…
We investigate the link between regularised self-transport problems and maximum likelihood estimation in Gaussian mixture models (GMM). This link suggests that self-transport followed by a clustering technique leads to principled estimators…
Quadratic regularization has emerged as a potential alternative to the popular entropic regularization in computational optimal transport, offering the theoretical advantage of producing sparse couplings through its hinge density structure.…
Consider a diffusion-free passive scalar $\theta$ being mixed by an incompressible flow $u$ on the torus $\mathbb{T}^d$. Our aim is to study how well this scalar can be mixed under an enstrophy constraint on the advecting velocity field.Our…
A linear stochastic continuity equation with non-regular coefficients is considered. We prove existence and uniqueness of strong solution, in the probabilistic sense, to the Cauchy problem when the vector field has low regularity, in which…
We derive rates of convergence for the mixing of operators under infinitely divisible measures in the framework of linear dynamics on Banach spaces. Our approach is based on the characterization of mixing in terms of codifference…
This article presents a general approximation-theoretic framework to analyze measure transport algorithms for probabilistic modeling. A primary motivating application for such algorithms is sampling -- a central task in statistical…
This paper is concerned with a posteriori error bounds for linear transport equations and related questions of contriving corresponding adaptive solution strategies in the context of Discontinuous-Petrov-Galerkin schemes. After indicating…
We present a framework for the solution of Boltzmann's equation in the swarm limit for arbitrary mass ratio, allowing for solutions of electron or ion transport. An arbitrary basis set can be used in the framework, which is achieved by…
This article deals with the observation problem in traffic flow theory. The model used is the semilinear viscous Burgers equation. Instead of using the traditional fixed sensors to estimate the state of the traffic at given points, the…
We develop a new approach to velocity averaging lemmas based on the dispersive properties of the kinetic transport operator. This method yields unprecedented sharp results, which display, in some cases, a gain of one full derivative.…
This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that…