Related papers: Smooth Aggregation for Difficult Stretched Mesh an…
Simulation of multiphase poromechanics involves solving a multi-physics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also…
Transfer Learning aims to optimally aggregate samples from a target distribution, with related samples from a so-called source distribution to improve target risk. Multiple procedures have been proposed over the last two decades to address…
We consider convex optimization with non-smooth objective function and log-concave sampling with non-smooth potential (negative log density). In particular, we study two specific settings where the convex objective/potential function is…
We propose a new algorithm for Adaptive Finite Element Methods (AFEMs) based on smoothing iterations (S-AFEM), for linear, second-order, elliptic partial differential equations (PDEs). The algorithm is inspired by the ascending phase of the…
Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that…
This paper addresses the challenging issue of symmetry in mixed-integer convex optimization problems, which frequently arise in real-world applications such as the unit commitment problem. Although variable aggregation techniques have been…
The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference…
In this paper, we develop a unified convergence analysis framework for the Accelerated Smoothed GAp ReDuction algorithm (ASGARD) introduced in [20, Tran-Dinh et al, 2015] Unlike[20], the new analysis covers three settings in a single…
A major challenge to implementing residential demand response is that of aligning the objectives of many households, each of which aims to minimize its payments and maximize its comfort level, while balancing this with the objectives of an…
In this paper, we introduce an inertial version of the Proximal Incremental Aggregated Gradient method (PIAG) for minimizing the sum of smooth convex component functions and a possibly nonsmooth convex regularization function.…
We propose a new self-adaptive, double-loop smoothing algorithm to solve composite, nonsmooth, and constrained convex optimization problems. Our algorithm is based on Nesterov's smoothing technique via general Bregman distance functions. It…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
In this paper, we introduce some adaptive methods for solving variational inequalities with relatively strongly monotone operators. Firstly, we focus on the modification of the recently proposed, in smooth case [1], adaptive numerical…
In this paper, we present a monolithic multigrid method for the efficient solution of flow problems in fractured porous media. Specifically, we consider a mixed-dimensional model which couples Darcy flow in the porous matrix with…
In this paper, we propose a proximal gradient method and an accelerated proximal gradient method for solving composite optimization problems, where the objective function is the sum of a smooth and a convex, possibly nonsmooth, function. We…
In this paper, we study the proximal incremental aggregated gradient(PIAG) algorithm for minimizing the sum of L-smooth nonconvex component functions and a proper closed convex function. By exploiting the L-smooth property and with the help…
A class of monotone operator equations, which can be decomposed into sum of the gradient of a strongly convex function and a linear and skew-symmetric operator, is considered in this work. Based on discretization of the generalized gradient…
We study the evolution of solidification microstructures using a phase-field model computed on an adaptive, finite element grid. We discuss the details of our algorithm and show that it greatly reduces the computational cost of solving the…
Ensembles of artificial neural networks show improved generalization capabilities that outperform those of single networks. However, for aggregation to be effective, the individual networks must be as accurate and diverse as possible. An…
Isogeometric Analysis is a high-order discretization method for boundary value problems that uses a number of degrees of freedom which is as small as for a low-order method. Standard isogeometric discretizations require a global…