Related papers: Is the Multigrid Method Fault Tolerant? The Two-Gr…
In smart electrical grids, fault detection tasks may have a high impact on society due to their economic and critical implications. In the recent years, numerous smart grid applications, such as defect detection and load forecasting, have…
With the increasing complexity of computing systems, complete hardware reliability can no longer be guaranteed. We need, however, to ensure overall system reliability. One of the most important features of artificial neural networks is…
In this article we consider two-grid finite element methods for solving semilinear interface problems in d space dimensions, for d=2 or d=3. We first describe in some detail the target problem class with discontinuous diffusion…
Supercomputing systems today often come in the form of large numbers of commodity systems linked together into a computing cluster. These systems, like any distributed system, can have large numbers of independent hardware components…
The convergence of multigrid methods degrades significantly if a small number of low quality cells are present in a finite element mesh, and this can be a barrier to the efficient and robust application of multigrid on complicated geometric…
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…
To mitigate the vulnerability of distribution grids to severe weather events, some electric utilities use preemptive de-energization as the primary line of defense, causing significant power outages. In such instances, networked microgrids…
The functionality of electronic circuits can be seriously impaired by the occurrence of dynamic hardware faults. Particularly, for digital ultra low-power systems, a reduced safety margin can increase the probability of dynamic failures.…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
Given a multigrid procedure for linear systems with coefficient matrices $A_n$, we discuss the optimality of a related multigrid procedure with the same smoother and the same projector, when applied to properly related algebraic problems…
Multigrid methods have proven to be an invaluable tool to efficiently solve large sparse linear systems arising in the discretization of partial differential equations (PDEs). Algebraic multigrid methods and in particular adaptive algebraic…
Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the…
The robustness of distributed optimization is an emerging field of study, motivated by various applications of distributed optimization including distributed machine learning, distributed sensing, and swarm robotics. With the rapid…
For many linear and nonlinear systems that arise from the discretization of partial differential equations the construction of an efficient multigrid solver is a challenging task. Here we present a novel approach for the optimization of…
For many types of integrated circuits, accepting larger failure rates in computations can be used to improve energy efficiency. We study the performance of faulty implementations of certain deep neural networks based on pessimistic and…
Although multigrid is asymptotically optimal for solving many important partial differential equations, its efficiency relies heavily on the careful selection of the individual algorithmic components. In contrast to recent approaches that…
This paper addresses the problem of estimating multiplicative fault signals in linear time-invariant systems by processing its input and output variables, as well as designing an input signal to maximize the accuracy of such estimates. The…
An active approach to fault tolerance is essential for robot swarms to achieve long-term autonomy. Previous efforts have focused on responding to spontaneous electro-mechanical faults and failures. However, many faults occur gradually over…
Bias is a common problem inherent in recommender systems, which is entangled with users' preferences and poses a great challenge to unbiased learning. For debiasing tasks, the doubly robust (DR) method and its variants show superior…
Energy increasingly constrains modern computer hardware, yet protecting computations and data against errors costs energy. This holds at all scales, but especially for the largest parallel computers being built and planned today. As…