Related papers: Dynamic Optimal Transport with Mixed Boundary Cond…

Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…

We formulate a finite-particle method of mass transport that accounts for general mixed boundary conditions. The particle method couples a geometrically-exact treatment of advection; Wasserstein gradient-flow dynamics; and a…

In this paper, we consider a primal-dual domain decomposition method for total variation regularized problems appearing in mathematical image processing. The model problem is transformed into an equivalent constrained minimization problem…

In this paper, we propose a numerical method to solve the classic $L^2$-optimal transport problem. Our algorithm is based on use of multiple shooting, in combination with a continuation procedure, to solve the boundary value problem…

Entropic optimal transport (EOT) in continuous spaces with quadratic cost is a classical tool for solving the domain translation problem. In practice, recent approaches optimize a weak dual EOT objective depending on a single potential, but…

We generalize the two-channel (Edwards) fermion-boson model describing quantum transport in a background medium to the more realistic case of dispersive bosons. Using the variational exact diagonalization technique, we numerically solve the…

A new pairwise cost function is proposed for the optimal transport barycenter problem, adopting the form of the minimal action between two points, with a Lagrangian that takes into account an underlying probability distribution. Under this…

Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it…

We consider the optimal transport problem over convex costs arising from optimal control of linear time-invariant(LTI) systems when the initial and target measures are assumed to be supported on the set of equilibrium points of the LTI…

Combinatorial optimization problems are typically formulated using Quadratic Unconstrained Binary Optimization (QUBO), where constraints are enforced through penalty terms that introduce auxiliary variables and rapidly increase Hamiltonian…

Consider the unsteady neutron transport equation with diffusive boundary condition in 2D convex domains. We establish the diffusive limit with both initial layer and boundary layer corrections. The major difficulty is the lack of regularity…

We consider two different variational models of transport networks, the so-called branched transport problem and the urban planning problem. Based on a novel relation to Mumford-Shah image inpainting and techniques developed in that field,…

Predicting the charged particle transport properties of warm dense matter / hot dense plasma mixtures is a challenge for analytical models. High accuracy ab initio methods are more computationally expensive, but can provide critical insight…

Consider the steady neutron transport equation in 2D convex domains with in-flow boundary condition. In this paper, we establish the diffusive limit while the boundary layers are present. Our contribution relies on a delicate decomposition…

We propose a new variational model for non-linear image fusion. Our approach is based on the use of an osmosis energy term related to the one studied in Vogel et al. (2013) and Weickert et al. (2013) The minimization of the proposed…

We derive new equations using the mixed-frame approach for one- and two-dimensional (axisymmetric) time-dependent radiation transport and the associated couplings with matter. Our formulation is multi-group and multi-angle and includes…

In this paper, we investigate an optimal design problem motivated by some issues arising in population dynamics. In a nutshell, we aim at determining the optimal shape of a region occupied by resources for maximizing the survival ability of…

We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…

Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…

We introduce a new technique, which we call the boundary method, for solving semi-discrete optimal transport problems with a wide range of cost functions. The boundary method reduces the effective dimension of the problem, thus improving…