Related papers: A Nonoverlapping Domain Decomposition Method for E…

In a recent paper [{\em F. Bernal, J. Mor\'on-Vidal and J.A. Acebr\'on, Comp.$\&$ Math. App. 146:294-308 (2023)}] an hybrid supercomputing algorithm for elliptic equations has been put forward. The idea is that the interfacial nodal…

This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…

Recurrent neural networks (RNN) have been successfully applied to various sequential decision-making tasks, natural language processing applications, and time-series predictions. Such networks are usually trained through back-propagation…

Diffusion Language Models (DLMs) offer attractive advantages over Auto-Regressive (AR) models, such as full-attention parallel decoding and flexible generation. However, standard DLM training uses a static, single-step masked prediction…

An efficient strategy to construct physics-based local surrogate models for parametric linear elliptic problems is presented. The method relies on proper generalized decomposition (PGD) to reduce the dimensionality of the problem and on an…

Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…

By integrating physics-informed neural network (PINN) techniques with domain decomposition method, a deep domain decomposition method is presented for solving elliptic variational inequality problems. Based on the Ritz variation method, the…

Elliptic partial differential equations (PDEs) with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electro-magnetic field propagation on heterogeneous media, and diffusion…

Deep Learning (DL) is a two-step classification model that consists feature learning, generating feature representations using unsupervised ways and the supervised learning stage at the last step of model using at least two hidden layers on…

In this paper, we propose and test a novel diagonal sweeping domain decomposition method (DDM) with source transfer for solving the high-frequency Helmholtz equation in $\mathbb{R}^n$. In the method the computational domain is partitioned…

Ensemble approaches introduced in the Extreme Learning Machine (ELM) literature mainly come from methods that relies on data sampling procedures, under the assumption that the training data are heterogeneously enough to set up diverse base…

Recent years, transfer learning has attracted much attention in the community of machine learning. In this paper, we mainly focus on the tasks of parameter transfer under the framework of extreme learning machine (ELM). Unlike the existing…

Deep Metric Learning (DML) learns a non-linear semantic embedding from input data that brings similar pairs together while keeping dissimilar data away from each other. To this end, many different methods are proposed in the last decade…

Differential privacy has become a cornerstone in the development of privacy-preserving learning algorithms. This work addresses optimizing differentially private kernel learning within the empirical risk minimization (ERM) framework. We…

We present DeepFDM, a differentiable finite-difference framework for learning spatially varying coefficients in time-dependent partial differential equations (PDEs). By embedding a classical forward-Euler discretization into a convolutional…

Although extreme learning machine (ELM) has been successfully applied to a number of pattern recognition problems, it fails to pro-vide sufficient good results in hyperspectral image (HSI) classification due to two main drawbacks. The first…

The popularity of algorithms based on Extreme Learning Machine (ELM), which can be used to train Single Layer Feedforward Neural Networks (SLFN), has increased in the past years. They have been successfully applied to a wide range of…

Dimensionality reduction (DR) plays a vital role in the visual analysis of high-dimensional data. One main aim of DR is to reveal hidden patterns that lie on intrinsic low-dimensional manifolds. However, DR often overlooks important…

The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…

Due to the nonlinear distortion in Orthogonal frequency division multiplexing (OFDM) systems, the timing synchronization (TS) performance is inevitably degraded at the receiver. To relieve this issue, an extreme learning machine (ELM)-based…