Related papers: Matrix Analysis of Tracer Transport
This paper introduces a first-order method for solving optimal powered descent guidance (PDG) problems, that directly handles the nonconvex constraints associated with the maximum and minimum thrust bounds with varying mass and the pointing…
We consider the finite horizon optimal steering of the joint state probability distribution subject to the angular velocity dynamics governed by the Euler equation. The problem and its solution amounts to controlling the spin of a rigid…
We develop a computational method based on an Eulerian field called the "reference map", which relates the current location of a material point to its initial. The reference map can be discretized to permit finite-difference simulation of…
In this paper, we propose an inexact perturbed path-following algorithm in the framework of Lagrangian dual decomposition for solving large-scale structured convex optimization problems. Unlike the exact versions considered in literature,…
In this article we show how ideas, methods and results from optimal transportation can be used to study various aspects of the stationary measuresof Iterated Function Systems equipped with a probability distribution. We recover a classical…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
We provide a novel methodology for computing the most likely path taken by drifters between arbitrary fixed locations in the ocean. We also provide an estimate of the travel time associated with this path. Lagrangian pathways and travel…
This paper proposes an efficient numerical optimization approach for solving dynamic optimal transport (DOT) problems on general smooth surfaces, computing both the quadratic Wasserstein distance and the associated transportation path.…
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…
The optimal (Monge-Kantorovich) transportation problem is discussed from several points of view. The Lagrangian formulation extends the action of the {\em Lagrangian} $L(v,x,t)$ from the set of orbits in $\R^n$ to a set of measure-valued…
This article devises a new numerical method for first-order transport problems by using the primal-dual weak Galerkin (PD-WG) finite element method recently developed in scientific computing. The PD-WG method is based on a variational…
The estimation of the number of passengers with the identical journey is a common problem for public transport authorities. This problem is also known as the Origin- Destination estimation (OD) problem and it has been widely studied for the…
Optimal transport (OT) theory has attracted much attention in machine learning and signal processing applications. OT defines a notion of distance between probability distributions of source and target data points. A crucial factor that…
Adapted optimal transport (AOT) problems are optimal transport problems for distributions of a time series where couplings are constrained to have a temporal causal structure. In this paper, we develop computational tools for solving AOT…
In many scientific fields imaging is used to relate a certain physical quantity to other dependent variables. Therefore, images can be considered as a map from a real-world coordinate system to the non-negative measurements being acquired.…
The connection of Taylor maps and polynomial neural networks (PNN) to solve ordinary differential equations (ODEs) numerically is considered. Having the system of ODEs, it is possible to calculate weights of PNN that simulates the dynamics…
Given their flexibility and encouraging performance, deep-learning models are becoming standard for motion prediction in autonomous driving. However, with great flexibility comes a lack of interpretability and possible violations of…
Let R and S be two vectors of real numbers whose entries have the same sum. In the transportation problems one wishes to find a matrix A with row sum vector R and column sum vector S. If, in addition, the two vectors only contain…
This paper investigates the semi-discrete optimal transport (OT) problem with entropic regularization. We characterize the solution using a governing, well-posed ordinary differential equation (ODE). This naturally yields an algorithm to…
We study the optimal transport problem for pairs of stationary finite-state Markov chains, with an emphasis on the computation of optimal transition couplings. Transition couplings are a constrained family of transport plans that capture…