Related papers: Efficient Multiscale Methods for Highly Heterogene…
Analyzing electromagnetic fields in complex, multi-material environments presents substantial computational challenges. To address these, we propose a hybrid numerical method that couples discrete exterior calculus (DEC) with surface…
Heterogeneous graphs are ubiquitous in real-world applications because they can represent various relationships between different types of entities. Therefore, learning embeddings in such graphs is a critical problem in graph machine…
We present a novel approach for computing a variant of eigenvector centrality for multilayer networks with inter-layer constraints on node importance. Specifically, we consider a multilayer network defined by multiple edge-weighted,…
Estimating accurate high-dimensional transformations remains very challenging, especially in a clinical setting. In this paper, we introduce a multiscale parameterization of deformations to enhance registration and atlas estimation in the…
We present three multi-scale similarity learning architectures, or DeepSim networks. These models learn pixel-level matching with a contrastive loss and are agnostic to the geometry of the considered scene. We establish a middle ground…
Most statistical models for networks focus on pairwise interactions between nodes. However, many real-world networks involve higher-order interactions among multiple nodes, such as co-authors collaborating on a paper. Hypergraphs provide a…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
We present a PDE-based approach for the multidimensional extrapolation of smooth scalar quantities across interfaces with kinks and regions of high curvature. Unlike the commonly used method of [2] in which normal derivatives are…
We propose a new framework for identifying mechanical properties of heterogeneous materials without a closed-form constitutive equation. Given a full-field measurement of the displacement field, for instance as obtained from digital image…
In recent years, the direction of the study of networks in which connections correspond to the mutual influences of nodes has been developed. Many works have been devoted to the study of such complex networks, but most often they relate to…
Interface problems depict many fundamental physical phenomena and widely apply in the engineering. However, it is challenging to develop efficient fully decoupled numerical methods for solving degenerate interface problems in which the…
We propose a multiscale approach for an elliptic multiscale setting with general unstructured diffusion coefficients that is able to achieve high-order convergence rates with respect to the mesh parameter and the polynomial degree. The…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
This paper presents a high-accuracy higher-order multiscale method for solving multi-continuum problems in in highly heterogeneous media. First, microscopic unit cell functions are defined, leading to the derivation of macroscopic…
We propose a neural network-based approach to the homogenization of multiscale problems. The proposed method uses a derivative-free formulation of a training loss, which incorporates Brownian walkers to find the macroscopic description of a…
Multilayer networks have become increasingly ubiquitous across diverse scientific fields, ranging from social sciences and biology to economics and international relations. Despite their broad applications, the inferential theory for…
In recent years, tremendous progress has been made on numerical algorithms for solving partial differential equations (PDEs) in a very high dimension, using ideas from either nonlinear (multilevel) Monte Carlo or deep learning. They are…
The problem of excessive pilot overhead required for uplink massive MIMO channel estimation is well known, let alone when it is considered along with wideband (OFDM) transmissions. Towards channel estimators that are both efficient and…
Representation learning of networks has witnessed significant progress in recent times. Such representations have been effectively used for classic network-based machine learning tasks like node classification, link prediction, and network…
Recently, CNN based end-to-end deep learning methods achieve superiority in Image Dehazing but they tend to fail drastically in Non-homogeneous dehazing. Apart from that, existing popular Multi-scale approaches are runtime intensive and…