Related papers: Operator splitting algorithm for structured popula…
The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schr\"{o}dinger equations. However, when applied to certain nonlinear time-dependent Schr\"{o}dinger equations, this algorithm loses…
A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…
We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has so far…
Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…
This work develops an active learning framework to intelligently enrich data-driven reduced-order models (ROMs) of parametric dynamical systems, which can serve as the foundation of virtual assets in a digital twin. Data-driven ROMs are…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
We propose a geometric framework to describe and analyze a wide array of operator splitting methods for solving monotone inclusion problems. The initial inclusion problem, which typically involves several operators combined through…
Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite element method for solving such problems. We begin by introducing…
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…
The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…
Euler's elastica model has a wide range of applications in Image Processing and Computer Vision. However, the non-convexity, the non-smoothness and the nonlinearity of the associated energy functional make its minimization a challenging…
This work presents a new three-operator splitting method to handle monotone inclusion and convex optimization problems. The proposed splitting serves as another natural extension of the Douglas-Rachford splitting technique to problems…
We study operator-splitting schemes for approximating Koopman generators of linear semigroups induced by nonlinear flows, a framework originating with Dorroh and Neuberger. Building on ideas of Lie, Kowalewski, and Gr\"{o}bner, we analyze…
Distributed statistical learning has become a popular technique for large-scale data analysis. Most existing work in this area focuses on dividing the observations, but we propose a new algorithm, DDAC-SpAM, which divides the features under…
In this paper we develop a statistical theory and an implementation of deep learning models. We show that an elegant variable splitting scheme for the alternating direction method of multipliers optimises a deep learning objective. We allow…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
Sliced optimal transport, which is basically a Radon transform followed by one-dimensional optimal transport, became popular in various applications due to its efficient computation. In this paper, we deal with sliced optimal transport on…
Operator splitting schemes have been successfully used in computational sciences to reduce complex problems into a series of simpler subproblems. Since 1950s, these schemes have been widely used to solve problems in PDE and control.…