Related papers: Variational models of robust optimal transport
Current research on robust trajectory planning for autonomous agents aims to mitigate uncertainties arising from disturbances and modeling errors while ensuring guaranteed safety. Existing methods primarily utilize stochastic optimal…
In this article, we consider transport networks with uncertain demands. Network dynamics are given by linear hyperbolic partial differential equations and suitable coupling conditions, while demands are incorporated as solutions to…
Human mobility, enabled by diverse transportation modes, is fundamental to urban functionality. Studying these movements across scales-from microscopic to macroscopic-yields valuable insights into urban dynamics. Local adaptation and…
We introduce a constrained optimal transport problem where origins $x$ can only be transported to destinations $y\geq x$. Our statistical motivation is to describe the sharp upper bound for the variance of the treatment effect $Y-X$ given…
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex…
The formation and development of oscillations is an important traffic flow phenomenon. Recent studies found that along a vehicle platoon described in the Lagrangian specification, traffic oscillations grow in a concave way. Since stationary…
This paper treats an optimal scheduling problem of control nodes in networked systems. We newly introduce both the L0 and l0 constraints on control inputs to extract a time-varying small number of effective control nodes. As the cost…
We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict new matching in various matching…
Motivated by developments in renewable energy and smart grids, we formulate a stylized mathematical model of a transport network with stochastic load fluctuations. Using an affine control rule, we explore the trade-off between the number of…
The contribution of this paper is a generalized formulation of correctional learning using optimal transport, which is about how to optimally transport one mass distribution to another. Correctional learning is a framework developed to…
Express transportation network design is uncertain because origin--destination demand, travel time, operating cost, hub congestion, and realized sorting productivity vary over time. Existing multi-topology express network models usually…
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal transport have been…
Disaster management is a complex problem demanding sophisticated modeling approaches. We propose utilizing a hybrid method involving inverse optimization to parameterize the cost functions for a road network's traffic equilibrium problem…
Vascular networks are used across the kingdoms of life to transport fluids, nutrients and cellular material. A popular unifying idea for understanding the diversity and constraints of these networks is that the conduits making up the…
This paper proposes an adaptive lattice-based motion planning solution to address the problem of generating feasible trajectories for systems, represented by a linearly parameterizable non-linear model operating within a cluttered…
In this paper, we introduce a hierarchical decision-making framework for emerging mobility systems. Despite numerous studies focusing on optimizing vehicle flow, practical feasibility has often been overlooked. To address this gap, we…
The goal of robust motion planning consists of designing open-loop controls which optimally steer a system to a specific target region while mitigating uncertainties and disturbances which affect the dynamics. Recently, stochastic optimal…
This note outlines a mean-field approach to dynamic optimal transport problems based on the recently proposed McKean-Pontryagin maximum principle. Key aspects of the proposed methodology include i) avoidance of sampling over stochastic…
We introduce an efficient computational framework for solving a class of multi-marginal martingale optimal transport problems, which includes many robust pricing problems of large financial interest. Such problems are typically…
We consider the incompressible three-dimensional Euler equations for a vortex ring with Kelvin waves undergoing radially expanding Lagrangian transport. To clarify the fundamental mechanisms underlying nonlinear scale-local deformations of…