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Optimal transport (OT) theory provides a principled framework for modeling mass movement in applications such as mobility, logistics, and economics. Classical formulations, however, generally ignore capacity limits that are intrinsic in…
In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
Macroscopic traffic flow is stochastic, but the physics-informed deep learning methods currently used in transportation literature embed deterministic PDEs and produce point-valued outputs; the stochasticity of the governing dynamics plays…
The dynamic formulation of optimal transport, also known as the Benamou-Brenier formulation, has been extended to the unbalanced case by introducing a source term in the continuity equation. When this source term is penalized based on the…
We introduce the proximal optimal transport divergence, a novel discrepancy measure that interpolates between information divergences and optimal transport distances via an infimal convolution formulation. This divergence provides a…
The dynamical formulation of the optimal transport can be extended through various choices of the underlying geometry (kinetic energy), and the regularization of density paths (potential energy). These combinations yield different…
Recently, Papadakis et al. proposed an efficient primal-dual algorithm for solving the dynamic optimal transport problem with quadratic ground cost and measures having densities with respect to the Lebesgue measure. It is based on the fluid…
We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on…
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…
Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…
This paper proposes the theoretical grounds for emulating the Dynamic System Optimum with desired arrival times on regional networks, using aggregated traffic dynamics based on the Macroscopic Fundamental Diagram. We used a projection…
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…
We consider optimal transport based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss…
We investigate optimal mass transport problem of affine-nonlinear dynamical systems with input and density constraints. Three algorithms are proposed to tackle this problem, including two Uzawa-type methods and a splitting algorithm based…
Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…
We present a primal-dual dynamical formulation of the multi-marginal optimal transport problem for (semi-)convex cost functions. Even in the two-marginal setting, this formulation applies to cost functions not covered by the classical…
We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…
This paper offers an integrative data-driven physics-inspired approach to model and control traffic congestion in a resilient and efficient manner. While existing physics-based approaches commonly assign density and flow traffic states by…
Traffic on a circular road is described by dynamic programming equations associated to optimal control problems. By solving the equations analytically, we derive the relation between the average car density and the average car flow, known…