Related papers: Domain decomposition for entropic unbalanced optim…
Domain decomposition (DD) methods for solving time-dependent problems can be classified by (i) the method of domain decomposition used, (ii) the choice of decomposition operators (exchange of boundary conditions), and (iii) the splitting…
We consider the fundamental problem of sampling the optimal transport coupling between given source and target distributions. In certain cases, the optimal transport plan takes the form of a one-to-one mapping from the source support to the…
In the last fifteen years a significant progress was achieved by considering an entropic relaxation of the classical multi-partite optimal transport problem (MPOTP). The entropic relaxation gives rise to the rescaling problem of a given…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
This paper studies a combined space partitioning and network flow optimization problem, with applications to large-scale power, transportation, or communication systems. In dense wireless networks, one may want to simultaneously optimize…
While the optimal transport (OT) problem was originally formulated as a linear program, the addition of entropic regularization has proven beneficial both computationally and statistically, for many applications. The Sinkhorn fixed-point…
Entropic regularization provides a generalization of the original optimal transport problem. It introduces a penalty term defined by the Kullback-Leibler divergence, making the problem more tractable via the celebrated Sinkhorn algorithm.…
Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify…
The problem of robust distributed control arises in several large-scale systems, such as transportation networks and power grid systems. In many practical scenarios controllers might not have enough information to make globally optimal…
We characterize the solution to the entropically regularized optimal transport problem by a well-posed ordinary differential equation (ODE). Our approach works for discrete marginals and general cost functions, and in addition to two…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
In [Q. Liao et al., Commun. Math. Sci., 20(2022)], a linear-time Sinkhorn algorithm is developed based on dynamic programming, which significantly reduces the computational complexity involved in solving optimal transport problems. However,…
We show that the discrete Sinkhorn algorithm - as applied in the setting of Optimal Transport on a compact manifold - converges to the solution of a fully non-linear parabolic PDE of Monge-Ampere type, in a large-scale limit. The latter…
In this paper, we introduce a neural network-based method to address the high-dimensional dynamic unbalanced optimal transport (UOT) problem. Dynamic UOT focuses on the optimal transportation between two densities with unequal total mass,…
We derive iterative scaling algorithms of the Sinkhorn-Knopp (SK) type for constrained optimal transport. The constraints are in the form of prior-imposed zeroes in the transport plan. Based on classical Bregman arguments, we prove…
With recent advancements in computer hardware and software platforms, there has been a surge of interest in solving partial differential equations with deep learning-based methods, and the integration with domain decomposition strategies…
Numerically computing global policies to optimal control problems for complex dynamical systems is mostly intractable. In consequence, a number of approximation methods have been developed. However, none of the current methods can quantify…
We develop a fast and reliable method for solving large-scale optimal transport (OT) problems at an unprecedented combination of speed and accuracy. Built on the celebrated Douglas-Rachford splitting technique, our method tackles the…
In this paper, a green transportation location problem is considered with uncertain demand parameter. Increasing robustness influences the number of trucks for sending goods and products, and consequently, makes the air pollution enhance.…