Related papers: Large-Scale Wasserstein Gradient Flows
A relaxed notion of displacement convexity is defined and used to establish short time existence and uniqueness of Wasserstein gradient flows for higher order energy functionals. As an application, local and global well-posedness of…
The computation of Wasserstein gradient direction is essential for posterior sampling problems and scientific computing. The approximation of the Wasserstein gradient with finite samples requires solving a variational problem. We study the…
In this paper, we study the Wasserstein gradient flow structure of the porous medium equation. We prove that, for the case of $q$-Gaussians on the real line, the functional derived by the JKO-discretization scheme is asymptotically…
We design and compute first-order implicit-in-time variational schemes with high-order spatial discretization for initial value gradient flows in generalized optimal transport metric spaces. We first review some examples of gradient flows…
We introduce a family of reversible fragmentating-coagulating processes of particles of varying size-scaled diffusivity with strictly local interaction on the real line as mathematically rigorous description of colloidal motion of fluids.…
This paper focuses on the contextual optimization problem where a decision is subject to some uncertain parameters and covariates that have some predictive power on those parameters are available before the decision is made. More…
Many studies have been conducted on flows of probability measures, often in terms of gradient flows. We utilize a generalized notion of derivatives with respect to time to model the instantaneous evolution of empirically observed…
We study a natural Wasserstein gradient flow on manifolds of probability distributions with discrete sample spaces. We derive the Riemannian structure for the probability simplex from the dynamical formulation of the Wasserstein distance on…
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…
We consider a minimax problem motivated by distributionally robust optimization (DRO) when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization…
We develop a new computational framework to solve the partial differential equations (PDEs) governing the flow of the joint probability density functions (PDFs) in continuous-time stochastic nonlinear systems. The need for computing the…
We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the…
In this work, we investigate links between the formulation of the flow of marginals of reversible diffusion processes as gradient flows in the space of probability measures and path wise large deviation principles for sequences of such…
Diffusion regulates numerous natural processes and the dynamics of many successful generative models. Existing models to learn the diffusion terms from observational data rely on complex bilevel optimization problems and model only the…
We consider the problem of sampling from a probability distribution $\pi$. It is well known that this can be written as an optimisation problem over the space of probability distribution in which we aim to minimise the Kullback--Leibler…
Understanding the risks posed by extreme rainfall events requires analysis of precipitation fields with high resolution (to assess localized hazards) and extensive historical coverage (to capture sufficient examples of rare occurrences).…
Wasserstein-Fisher-Rao (WFR) gradient flows have been recently proposed as a powerful sampling tool that combines the advantages of pure Wasserstein (W) and pure Fisher-Rao (FR) gradient flows. Existing algorithmic developments implicitly…
We reveal a precise mathematical framework about a new family of generative models which we call Gradient Flow Drifting. With this framework, we prove an equivalence between the recently proposed Drifting Model and the Wasserstein gradient…
In this paper, we study efficient approximate sampling for probability distributions known up to normalization constants. We specifically focus on a problem class arising in Bayesian inference for large-scale inverse problems in science and…
We consider a nonlinear degenerate convection-diffusion equation with inhomogeneous convection and prove that its entropy solutions in the sense of Kru\v{z}kov are obtained as the - a posteriori unique - limit points of the JKO variational…