相关论文: Another Look at Neural Multigrid

Modern machine learning suffers from catastrophic forgetting when learning new classes incrementally. The performance dramatically degrades due to the missing data of old classes. Incremental learning methods have been proposed to retain…

In this paper, we introduce the neural empirical interpolation method (NEIM), a neural network-based alternative to the discrete empirical interpolation method for reducing the time complexity of computing the nonlinear term in a reduced…

High performance grid computing is a key enabler of large scale collaborative computational science. With the promise of exascale computing, high performance grid systems are expected to incur electricity bills that grow super-linearly over…

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…

Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…

Join ordering is the NP-hard problem of selecting the most efficient order in which to evaluate joins (conjunctive, binary operators) in a database query. Because query execution performance critically depends on this choice, join ordering…

Rearranging the rows or columns of a sparse matrix using an appropriate ordering can significantly reduce fill-ins, i.e., new nonzeros introduced during matrix factorization, decreasing memory usage and runtime. However, finding an ordering…

We propose a multigrid extension of convolutional neural networks (CNNs). Rather than manipulating representations living on a single spatial grid, our network layers operate across scale space, on a pyramid of grids. They consume multigrid…

We propose a simple and efficient one-way multigrid method for self-consistent electronic structure calculations based on iterative diagonalization. Total energy calculations are performed on several different levels of grids starting from…

A set of accelerated first order algorithms with memory are proposed for minimising strongly convex functions. The algorithms are differentiated by their use of the iterate history for the gradient step. The increased convergence rate of…

Microgrids have more operational flexibilities as well as uncertainties than conventional power grids, especially when renewable energy resources are utilized. An energy storage based feedback controller can compensate undesired dynamics of…

The current deep learning model is of a single-grade, that is, it learns a deep neural network by solving a single nonconvex optimization problem. When the layer number of the neural network is large, it is computationally challenging to…

In this work, we show that for linearly constrained optimization problems the primal-dual hybrid gradient algorithm, analyzed by Chambolle and Pock [3], can be written as an entirely primal algorithm. This allows us to prove convergence of…

This paper proposes a mode multigrid (MMG) method, and applies it to accelerate the convergence of the steady state flow on unstructured grids. The dynamic mode decomposition (DMD) technique is used to analyze the convergence process of…

Machine learning techniques are used to predict theoretical constraints such as unitarity and boundedness from below in extensions of the Standard Model. This approach has proven effective for models incorporating additional SU(2) scalar…

We combine the multigrid (MG) method with state-of-the-art concepts from the variational formulation of the numerical renormalization group. The resulting MG renormalization (MGR) method is a natural generalization of the MG method for…

In some cases, computational benefit can be gained by exploring the hyper parameter space using a deterministic set of grid points instead of a Markov chain. We view this as a numerical integration problem and make three unique…

We propose a highly parallel primal-dual algorithm for the multicut (a.k.a. correlation clustering) problem, a classical graph clustering problem widely used in machine learning and computer vision. Our algorithm consists of three steps…

In this work, we develop Non-Intrusive Reduced Order Models (NIROMs) that combine Proper Orthogonal Decomposition (POD) with a Radial Basis Function (RBF) interpolation method to construct efficient reduced order models for time-dependent…

Can a neural network minimizing cross-entropy learn linearly separable data? Despite progress in the theory of deep learning, this question remains unsolved. Here we prove that SGD globally optimizes this learning problem for a two-layer…