相关论文: Multigrid meets Neural Nets

This paper presents a two-layer, four-level distributed control method for networked microgrid (NMG) systems, taking into account the proprietary nature of microgrid (MG) owners. The proposed control architecture consists of a MG-control…

In this paper, we present a novel data-free method for merging neural networks in weight space. Differently from most existing works, our method optimizes for the permutations of network neurons globally across all layers. This allows us to…

Neural-networks have seen a surge of interest for the interpretation of seismic images during the last few years. Network-based learning methods can provide fast and accurate automatic interpretation, provided there are sufficiently many…

Large linear systems with sparse, non-symmetric matrices arise in the modeling of Markov chains or in the discretization of convection-diffusion problems. Due to their potential to solve sparse linear systems with an effort that is linear…

A fast multigrid solver is presented for high-order accurate Stokes problems discretised by local discontinuous Galerkin (LDG) methods. The multigrid algorithm consists of a simple V-cycle, using an element-wise block Gauss-Seidel smoother.…

We conduct experimental simulations of many body quantum systems using a \emph{hybrid} classical-quantum algorithm. In our setup, the wave function of the transverse field quantum Ising model is represented by a restricted Boltzmann…

This paper presents a learnable solver tailored to iteratively solve sparse linear systems from discretized partial differential equations (PDEs). Unlike traditional approaches relying on specialized expertise, our solver streamlines the…

As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…

Time-evolving or temporal graphs gain more and more popularity when studying the behavior of complex networks. In this context, the multistage view on computational problems is among the most natural frameworks. Roughly speaking, herein one…

We propose a sparse interpolation construction and a practical coarsening algorithm for the algebraic multigrid (AMG) method, tailored towards H(curl). Building on the generalized AMG framework, we introduce an interior/exterior splitting…

In recent years, graph neural networks (GNNs) have shown tremendous promise in solving problems in high energy physics, materials science, and fluid dynamics. In this work, we introduce a new application for GNNs in the physical sciences:…

Deep neural network has recently shown very promising applications in different research directions and attracted the industry attention as well. Although the idea was introduced in the past but just recently the main limitation of using…

We investigate the use of deep neural networks to control complex nonlinear dynamical systems, specifically the movement of a rigid body immersed in a fluid. We solve the Navier Stokes equations with two way coupling, which gives rise to…

Algebraic multigrid (AMG) is known to be an effective solver for many sparse symmetric positive definite (SPD) linear systems. For SPD systems, the convergence theory of AMG is well-understood in terms of the $A$-norm, but in a nonsymmetric…

The multi-timestep command governor (MCG) is an add-on algorithm that enforces constraints by modifying, at each timestep, the reference command to a pre-stabilized control system. The MCG can be interpreted as a Model-Predictive Control…

Application of multigrid solvers in shifted linear systems is studied. We focus on accelerating the rational approximation needed for simulating single flavor operators. This is particularly useful, in the case of twisted mass fermions for…

The transfer learning of a neural network is one of its most outstanding aspects and has given supervised learning with neural networks a prominent place in data science. Here we explore this feature in the context of strongly interacting…

Neural networks have been applied to the physical layer of wireless communication systems to solve complex problems. In millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems, hybrid precoding has been considered as…

Neural radiance fields (NeRF) have demonstrated the potential of coordinate-based neural representation (neural fields or implicit neural representation) in neural rendering. However, using a multi-layer perceptron (MLP) to represent a 3D…

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…