Related papers: Efficient Computation of Mean field Control based …
This papers shows the convergence of optimal control problems where the constraint function is discretised by a particle method. In particular, we investigate the viscous Burgers equation in the whole space $\mathbb R$ by using…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
This paper develops an approach for solving perpetual discounted optimal stopping problems for multidimensional diffusions, with special emphasis on the $d$-dimensional Wiener process. We first obtain some verification theorems for…
Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather…
The dynamical formulation of optimal transport, also known as Benamou-Brenier formulation or Computational Fluid Dynamics formulation, amounts to write the optimal transport problem as the optimization of a convex functional under a PDE…
This work analyzes a fully discrete mixed finite element method in a Banach space framework for solving nonstationary coupled fluid flow problems modeled by the Brinkman-Forchheimer equations, with applications to reverse osmosis. The model…
The solution of partial differential equations (PDEs) on complex domains often presents a significant computational challenge by requiring the generation of fitted meshes. The Diffuse Domain Method (DDM) is an alternative which reformulates…
We develop an immersed-boundary approach to modeling reaction-diffusion processes in dispersions of reactive spherical particles, from the diffusion-limited to the reaction-limited setting. We represent each reactive particle with a…
We study in this paper a variant of Wasserstein barycenter problem, which we refer to as tree-Wasserstein barycenter, by leveraging a specific class of ground metrics, namely tree metrics, for Wasserstein distance. Drawing on the tree…
Binary optimization, a representative subclass of discrete optimization, plays an important role in mathematical optimization and has various applications in computer vision and machine learning. Usually, binary optimization problems are…
In this work we propose a weighted hybridizable discontinuous Galerkin method (W-HDG) for drift-diffusion problems. By using specific exponential weights when computing the $L^2$ product in each cell of the discretization, we are able to…
A randomized version of the recently developed barycenter method for derivative--free optimization has desirable properties of a gradient search. We developed a complex version to avoid evaluations at high--gradient points. The method,…
Barycentric averaging is a principled way of summarizing populations of measures. Existing algorithms for estimating barycenters typically parametrize them as weighted sums of Diracs and optimize their weights and/or locations. However,…
In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…
Gradient flow in the 2-Wasserstein space is widely used to optimize functionals over probability distributions and is typically implemented using an interacting particle system with $n$ particles. Analyzing these algorithms requires showing…
This paper presents a new method for conditional probability density simulation. The method is design to work with unstructured data set when data are not characterized by the same covariates yet share common information. Specific examples…
We study a nonlinear, degenerate cross-diffusion model which involves two densities with two different drift velocities. A general framework is introduced based on its gradient flow structure in Wasserstein space to derive a notion of…
The goal of this work is to obtain optimal rates for the convergence problem in mean field control. Our analysis covers cases where the solutions to the limiting problem may not be unique nor stable. Equivalently the value function of the…
Optimal transport is a foundational problem in optimization, that allows to compare probability distributions while taking into account geometric aspects. Its optimal objective value, the Wasserstein distance, provides an important loss…
We consider the problem of optimizing hybrid structures (mixture of discrete and continuous input variables) via expensive black-box function evaluations. This problem arises in many real-world applications. For example, in materials design…