相关论文: Generalized Multiscale Finite Element Method for d…

The construction of local reduced-order models via multiscale basis functions has been an area of active research. In this paper, we propose online multiscale basis functions which are constructed using the offline space and the current…

Many existing statistical and machine learning tools for social network analysis focus on a single level of analysis. Methods designed for clustering optimize a global partition of the graph, whereas projection based approaches (e.g. the…

This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…

In this research, an online basis enrichment strategy for the constraint energy minimizing generalized multiscale finite element method in mixed formulation is proposed. The online approach is based on the technique of oversampling. One…

We introduce a general, analytical framework to express and to approximate partial differential equations (PDEs) numerically on graphs and networks of surfaces---generalized by the term hypergraphs. To this end, we consider PDEs on…

This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into…

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced-order methods are demanded. Combining these…

In this work, we present a general framework for the design and analysis of two-level AMG methods. The approach is to find a basis for locally optimal or quasi-optimal coarse space, such as the space of constant vectors for standard…

The paper addresses a numerical method for solving second order elliptic partial differential equations that describe fields inside heterogeneous media. The scope is general and treats the case of rough coefficients, i.e. coefficients with…

The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…

We consider a distributed estimation method in a setting with heterogeneous streams of correlated data distributed across nodes in a network. In the considered approach, linear models are estimated locally (i.e., with only local data)…

We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…

Distributed parameter estimation for large-scale systems is an active research problem. The goal is to derive a distributed algorithm in which each agent obtains a local estimate of its own subset of the global parameter vector, based on…

Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through…

Multilayer networks allow one to represent diverse and coupled connectivity patterns --- e.g., time-dependence, multiple subsystems, or both --- that arise in many applications and which are difficult or awkward to incorporate into standard…

Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…

Fiber network modeling can be used for studying mechanical properties of paper. The individual fibers and the bonds in-between constitute a detailed representation of the material. However, detailed microscale fiber network models must be…

Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural…

The rapid development of high-throughput technologies has enabled the generation of data from biological or disease processes that span multiple layers, like genomic, proteomic or metabolomic data, and further pertain to multiple sources,…

We propose a simple discrete time semi-supervised graph embedding approach to link prediction in dynamic networks. The learned embedding reflects information from both the temporal and cross-sectional network structures, which is performed…