We propose a globally convergent multilevel training method for deep residual networks
(ResNets). The devised method can be seen as a novel variant of the recursive multilevel …

Environmental mapping serves as a crucial element in Simultaneous Localization and
Mapping (SLAM) algorithms, playing a pivotal role in ensuring the accurate representation …

Among different functional data analyses, clustering analysis aims to determine underlying
groups of curves in the dataset when there is no information on the group membership of …

We consider the least-squares finite element method (lsfem) for systems of nonlinear
ordinary differential equations, and establish an optimal error estimate for this method when …

We consider three optimal control problems, which focus on continuous path-planning
applications, and each problem deals with a specific challenge. First, we introduce a new …

Abstract Neural Ordinary Differential Equations (Neural ODEs) are deep learning neural
networks with constraints specified by ordinary differential equations and initial values …