Related papers: Is the Multigrid Method Fault Tolerant? The Multil…
Multigrid is one of the most efficient methods for solving large-scale linear systems that arise from discretized partial differential equations. As a foundation for multigrid analysis, two-grid theory plays an important role in motivating…
This research paper investigates how machine learning-driven data replication strategies can enhance fault tolerance in large-scale distributed systems. Traditional replication methods, which rely on static configurations, often struggle to…
100% inverter-based renewable units are becoming more prevalent, introducing new challenges in the protection of microgrids that incorporate these resources. This is particularly due to low fault currents and bidirectional flows. Previous…
Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…
With the rapid advancements of deep learning in the past decade, it can be foreseen that deep learning will be continuously deployed in more and more safety-critical applications such as autonomous driving and robotics. In this context,…
Microgrids are being increasing deployed to improve the operational flexibility, resilience, coordinated-energy management capabilities, self-adequacy, and increased reliability of power systems. This strong market growth is also driven by…
This paper presents a multilevel convergence framework for multigrid-reduction-in-time (MGRIT) as a generalization of previous two-grid estimates. The framework provides a priori upper bounds on the convergence of MGRIT V- and F-cycles,…
This paper proposes a fully distributed termination method for distributed optimization algorithms solved by multiple agents. The proposed method guarantees terminating a distributed optimization algorithm after satisfying the global…
Constructing fast numerical solvers for partial differential equations (PDEs) is crucial for many scientific disciplines. A leading technique for solving large-scale PDEs is using multigrid methods. At the core of a multigrid solver is the…
In recent advances in solving the problem of transmission network expansion planning, the use of robust optimization techniques has been put forward, as an alternative to stochastic mathematical programming methods, to make the problem…
Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…
This paper introduces a novel geometric multigrid solver for unstructured curved surfaces. Multigrid methods are highly efficient iterative methods for solving systems of linear equations. Despite the success in solving problems defined on…
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…
In this paper, in an attempt to improve power grid resilience, a machine learning model is proposed to predictively estimate the component states in response to extreme events. The proposed model is based on a multi-dimensional Support…
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…
Existing or planned power grids need to evaluate survivability under extreme events, like a number of peak load overloading conditions, which could possibly cause system collapses (i.e. blackouts). For realistic extreme events that are…
In this paper, we examine the different measures of Fault Tolerance in a Distributed Simulated Annealing process. Optimization by Simulated Annealing on a distributed system is prone to various sources of failure. We analyse simulated…
The performance of finite element solvers on modern computer architectures is typically memory bound for sufficiently large problems. The main cause for this is that loading matrix elements from RAM into CPU cache is significantly slower…
A new high-level implementation independent functional fault model for control faults in microprocessors is introduced. The fault model is based on the instruction set, and is specified as a set of data constraints to be satisfied by test…
In many practical applications of numerical methods a substantial increase in efficiency can be obtained by using local grid refinement, since the solution is generally smooth in large parts of the domain and large gradients occur only…