Related papers: The back-and-forth method for Wasserstein gradient…
Seismic traveltime tomography represents a popular and useful tool for unravelling the structure of the subsurface across the scales. In this work we address the case where the forward model is represented by the eikonal equation and derive…
The Straight-Through (ST) estimator is a widely used technique for back-propagating gradients through discrete random variables. However, this effective method lacks theoretical justification. In this paper, we show that ST can be…
Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in practice, however, leading previous work to restrict their…
Recently, optimization on the Riemannian manifold have provided valuable insights to the optimization community. In this regard, extending these methods to to the Wasserstein space is of particular interest, since optimization on…
We study Fokker--Planck equations with symmetric, positive definite mobility matrices capturing diffusion in heterogeneous environments. A weighted Wasserstein metric is introduced for which these equations are gradient flows. This metric…
We study fast and reliable generative transport for the 3D KS (Keller-Segel) and KPP (Kolmogorov-Petrovsky-Piskunov) equations in the presence of fluid flows with the goal to approximate the map between initial and terminal distributions…
We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances…
This paper presents a novel adjoint solver for differentiable fluid simulation based on bidirectional flow maps. Our key observation is that the forward fluid solver and its corresponding backward, adjoint solver share the same flow map as…
We study the Fokker-Planck equation as the hydrodynamic limit of a stochastic particle system on one hand and as a Wasserstein gradient flow on the other. We write the rate functional, that characterizes the large deviations from the…
Wasserstein gradient flows have become a central tool for optimization problems over probability measures. A natural numerical approach is forward-Euler time discretization. We show, however, that even in the simple case where the energy…
Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…
We analyze some parabolic PDEs with different drift terms which are gradient flows in the Wasserstein space and consider the corresponding discrete-in-time JKO scheme. We prove with optimal transport techniques how to control the L p and L…
We study the particle method to approximate the gradient flow on the $L^p$-Wasserstein space. This method relies on the discretization of the energy introduced by [3] via nonoverlapping balls centered at the particles and preserves the…
The JKO scheme is a time-discrete scheme of implicit Euler type that allows to construct weak solutions of evolution PDEs which have a Wasserstein gradient structure. The purpose of this work is to study the effect of replacing the…
We give a comprehensive description of Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals $\mathcal F_\nu := \text{MMD}_K^2(\cdot, \nu)$ towards given target measures $\nu$ on the real line, where we focus on the…
We study the large deviation rate functional for the empirical distribution of independent Brownian particles with drift. In one dimension, it has been shown by Adams, Dirr, Peletier and Zimmer that this functional is asymptotically…
This paper presents a groundbreaking approach to causal inference by integrating continuous normalizing flows (CNFs) with parametric submodels, enhancing their geometric sensitivity and improving upon traditional Targeted Maximum Likelihood…
We propose a supervised learning scheme for the first order Hamilton--Jacobi PDEs in high dimensions. The scheme is designed by using the geometric structure of Wasserstein Hamiltonian flows via a density coupling strategy. It is…
In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While this approach also controls the distance between the posterior…
We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable…