Related papers: Domain Overlapping Algorithm with Nonlinear Mappin…

We present a non-overlapping, Schwarz-type domain decomposition method with a generalized interface condition, designed for physics-informed machine learning of partial differential equations (PDEs) in both forward and inverse contexts. Our…

This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…

Domain decomposition methods are widely used for the numerical solution of partial differential equations on high performance computers. We develop an adjoint-based a posteriori error analysis for both multiplicative and additive…

We propose a domain decomposition method for the efficient simulation of nonlocal problems. Our approach is based on a multi-domain formulation of a nonlocal diffusion problem where the subdomains share "nonlocal" interfaces of the size of…

Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One…

Bilevel optimization has gained significant attention in recent years due to its broad applications in machine learning. This paper focuses on bilevel optimization in decentralized networks and proposes a novel single-loop algorithm for…

This paper deals with the parallel simulation of delamination problems at the meso-scale by means of multi-scale methods, the aim being the Virtual Delamination Testing of Composite parts. In the non-linear context, Domain Decomposition…

In this paper the author introduces a new domain decomposition method for the solution of discretised integral equation eigenvalue problems. The new domain decomposition method is motivated by the so-called automated multi-level…

Remarkable results have been achieved by DCNN based self-supervised depth estimation approaches. However, most of these approaches can only handle either day-time or night-time images, while their performance degrades for all-day images due…

In this article, a novel approach for merging 3D point cloud maps in the context of egocentric multi-robot exploration is presented. Unlike traditional methods, the proposed approach leverages state-of-the-art place recognition and learned…

We study Benamou's domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove…

We study overlapping Schwarz methods for the Helmholtz equation posed in any dimension with large, real wavenumber and smooth variable wave speed. The radiation condition is approximated by a Cartesian perfectly-matched layer (PML). The…

The personalized PageRank algorithm is one of the most versatile tools for the analysis of networks. In spite of its ubiquity, maintaining personalized PageRank vectors when the underlying network constantly evolves is still a challenging…

Starting from a comparison of some established numerical algorithms for the computation of the eigenvalues (discrete or solitonic spectrum) of the non-Hermitian version of the Zakharov-Shabat spectral problem, this article delivers new…

We present a meshless Schwarz-type non-overlapping domain decomposition method based on artificial neural networks for solving forward and inverse problems involving partial differential equations (PDEs). To ensure the consistency of…

This work proposes a discretization of the acoustic wave equation with possibly oscillatory coefficients based on a superposition of discrete solutions to spatially localized subproblems computed with an implicit time discretization. Based…

Cooperative Co-evolution, through the decomposition of the problem space, is a primary approach for solving large-scale global optimization problems. Typically, when the subspaces are disjoint, the algorithms demonstrate significantly both…

(Hyper)Graph decomposition is a family of problems that aim to break down large (hyper)graphs into smaller sub(hyper)graphs for easier analysis. The importance of this lies in its ability to enable efficient computation on large and complex…

Domain adaptation for Cross-LiDAR 3D detection is challenging due to the large gap on the raw data representation with disparate point densities and point arrangements. By exploring domain-invariant 3D geometric characteristics and motion…

Decentralized Collaborative Simultaneous Localization And Mapping (C-SLAM) techniques often struggle to identify map overlaps due to significant viewpoint variations among robots. Motivated by recent advancements in 3D foundation models,…