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This article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two…
By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…
A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…
We propose a numerical method to find the optimal transport map between a measure supported on a lower-dimensional subset of R^d and a finitely supported measure. More precisely, the source measure is assumed to be supported on a simplex…
We study an optimal transport problem where, at some intermediate time, the mass is accelerated by either an external force field, or self-interacting. We obtain regularity of the velocity potential, intermediate density, and optimal…
In this paper, we develop a systematic framework for the time-sequential compression of dynamic probabilistic occupancy grids. Our approach leverages ideas from signal compression theory to formulate an optimization problem that searches…
This paper addresses the problem of optimally controlling nonlinear systems with norm-bounded disturbances and parametric uncertainties while robustly satisfying constraints. The proposed approach jointly optimizes a nominal nonlinear…
The field of dynamic graph algorithms aims at achieving a thorough understanding of real-world networks whose topology evolves with time. Traditionally, the focus has been on the classic sequential, centralized setting where the main…
Routing optimization is a relevant problem in many contexts. Solving directly this type of optimization problem is often computationally unfeasible. Recent studies suggest that one can instead turn this problem into one of solving a…
Emerging edge computing paradigms enable heterogeneous devices to collaborate on complex computation applications. However, for arbitrary heterogeneous edge networks, delay-optimal forwarding and computation offloading remains an open…
We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient…
In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…
We study network design problems for nonlinear and nonconvex flow models without controllable elements under load scenario uncertainties, i.e., under uncertain injections and withdrawals. To this end, we apply the concept of adjustable…
We introduce a convergent finite difference method for solving the optimal transportation problem on the sphere. The method applies to both the traditional squared geodesic cost (arising in mesh generation) and a logarithmic cost (arising…
Understanding neural dynamics is a central topic in machine learning, non-linear physics and neuroscience. However, the dynamics is non-linear, stochastic and particularly non-gradient, i.e., the driving force can not be written as gradient…
This paper proposes a simplified version of classical models for urban transportation networks, and studies the problem of controlling intersections with the goal of optimizing network-wide congestion. Differently from traditional…
Optimal transport is the problem of designing a joint distribution for two random variables with fixed marginals. In virtually the entire literature on this topic, the objective is to minimize expected cost. This paper is the first to study…
We introduce COPT, a novel distance metric between graphs defined via an optimization routine, computing a coordinated pair of optimal transport maps simultaneously. This gives an unsupervised way to learn general-purpose graph…
In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of…
This paper introduces a dynamic formulation of divergence-regularized optimal transport with weak targets on the path space. In our formulation, the classical relative entropy penalty is replaced by a general convex divergence, and terminal…