We present a new rank-adaptive tensor method to compute the numerical solution of high-
dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series …

In this paper, we study a nonlocal approximation of the time-dependent (local) Eikonal
equation with Dirichlet-type boundary conditions, where the kernel in the nonlocal problem …

In this paper, we propose a computationally tractable and provably convergent algorithm for
robust optimization, with application to robust learning. First, the distributional robust …

The numerical simulation of high-dimensional partial differential equations (PDEs) is a
challenging and important problem in science and engineering. Classical methods based …

The present paper is a continuation of a previous work with conditions for regularity of the
metric projection. Here we provide a full quantitative characterization of closed bodies in …

The current challenge of Deep Learning is no longer the computational power nor its scope
of application that has drastically widened in the couple last decades but the robustness of …