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We analyse a general class of bilevel problems, in which the upper-level problem consists in the minimization of a smooth objective function and the lower-level problem is to find the fixed point of a smooth contraction map. This type of…

Dense granular flows exhibit both surface deformation and secondary flows due to the presence of normal stress differences. Yet, a complete mathematical modelling of these two features is still lacking. This paper focuses on a steady…

In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…

The virtual element method (VEM) allows discretization of the problem domain with polygons in 2D. The polygons can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing…

Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…

We study the horizontal mean curvature flow in the Heisenberg group by using the level-set method. We prove the uniqueness, existence and stability of axisymmetric viscosity solutions of the level-set equation. An explicit solution is given…

MeanFlow offers a promising framework for one-step generative modeling by directly learning a mean-velocity field, bypassing expensive numerical integration. However, we find that the highly curved generative trajectories of existing models…

In this work is considered a spectral problem, involving a second order term on the domain boundary: the Laplace-Beltrami operator. A variational formulation is presented, leading to a finite element discretization. For the Laplace-Beltrami…

Classical theory for quasi-Newton schemes has focused on smooth deterministic unconstrained optimization while recent forays into stochastic convex optimization have largely resided in smooth, unconstrained, and strongly convex regimes.…

We present an hybrid VOF/embedded boundary method allowing to model two-phase flows in presence of solids with arbitrary shapes. The method relies on the coupling of existing methods: a geometric Volume of fluid (VOF) method to tackle the…

Multiphase flows are an important class of fluid flow and their study facilitates the development of diverse applications in industrial, natural, and biomedical systems. We consider a model that uses a continuum description of both phases…

This work is based upon a coupled, lattice-based continuum formulation that was previously applied to problems involving strong coupling between mechanics and mass transport; e.g. diffusional creep and electromigration. Here we discuss an…

Reinforcement learning has by now become well established in finding excellent flow control strategies for a variety of scenarios. Existing literature has focused on using a simple two-jet solution (and variants there-of) or a…

In this article we use the mean curvature flow with surgery to derive regularity estimates for the level set flow going past Brakke regularity in certain special conditions allowing for 2-convex regions of high density. We also show a…

Recently, meshless methods have become popular in numerically solving partial differential equations and have been employed to solve equations governing fluid flows, heat transfer, and species transport. In the present study, a numerical…

Mesh offsetting plays an important role in discrete geometric processing. In this paper, we propose a parallel feature-preserving mesh offsetting framework with variable distance. Different from the traditional method based on distance and…

Many contemporary applications in signal processing and machine learning give rise to structured non-convex non-smooth optimization problems that can often be tackled by simple iterative methods quite effectively. One of the keys to…

Federated learning is an efficient machine learning tool for dealing with heterogeneous big data and privacy protection. Federated learning methods with regularization can control the level of communications between the central and local…

This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…

In this paper, we examine a number of additive and multiplicative multilevel iterative methods and preconditioners in the setting of two-dimensional local mesh refinement. While standard multilevel methods are effective for uniform…