Related papers: An Efficient Algorithm for Matrix-Valued and Vecto…
Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms requires the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we…
This paper develops a computational framework for Multi-Period Martingale Optimal Transport (MMOT), addressing convergence rates, algorithmic efficiency, and financial calibration. Our contributions include: (1) Theoretical analysis: We…
We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than…
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…
Optimal transport methods have recently established state of the art accuracy and efficiency for holographic laser beam shaping. However, use of such methods is hindered by severe $\mathcal{O}(N^2)$ memory and $\mathcal{O}(N^2)$ time…
We present a new method to derive transport equations for quantum many-particle systems. This method uses an equation-of-motion technique and is applicable to systems with bosons and fermions, arbitrary interactions and time-dependent…
We propose a new framework for formulating optimal transport distances between Markov chains. Previously known formulations studied couplings between the entire joint distribution induced by the chains, and derived solutions via a reduction…
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…
A novel adaptive Markov chain Monte Carlo algorithm is presented. The algorithm utilizes sparsity in the partial correlation structure of a density to efficiently estimate the covariance matrix through the Cholesky factor of the precision…
In this manuscript, we introduce the tensor-train reduced basis method, a novel projection-based reduced-order model designed for the efficient solution of parameterized partial differential equations. While reduced-order models are widely…
We propose a balanced coarsening scheme for multilevel hypergraph partitioning. In addition, an initial partitioning algorithm is designed to improve the quality of k-way hypergraph partitioning. By assigning vertex weights through the LPT…
Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a…
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…
We present an efficient and parsimonious algorithm to solve mixed initial/final-value problems. The algorithm optimally limits the memory storage and the computational time requirements: with respect to a simple forward integration, the…
We introduce a new, quadratically convergent algorithm for finding maximum absolute value entries of tensors represented in the canonical format. The computational complexity of the algorithm is linear in the dimension of the tensor. We…
We show that under some widely believed assumptions, there are no higher-order algorithms for basic tasks in computational mathematics such as: Computing integrals with neural network integrands, computing solutions of a Poisson equation…
We consider the problem of solving the optimal transport problem between two empirical distributions with missing values. Our main assumption is that the data is missing completely at random (MCAR), but we allow for heterogeneous…
Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex…
Joint diagonalization, the process of finding a shared set of approximate eigenvectors for a collection of matrices, arises in diverse applications such as multidimensional harmonic analysis or quantum information theory. This task is…
We investigate in this work a versatile convex framework for multiple image segmentation, relying on the regularized optimal mass transport theory. In this setting, several transport cost functions are considered and used to match…