Related papers: HiDeNN-PGD: reduced-order hierarchical deep learni…

While much attention of neural network methods is devoted to high-dimensional PDE problems, in this work we consider methods designed to work for elliptic problems on domains $\Omega \subset \mathbb{R} ^d, $ $d=1,2,3$ in association with…

6D pose estimation of rigid objects is a long-standing and challenging task in computer vision. Recently, the emergence of deep learning reveals the potential of Convolutional Neural Networks (CNNs) to predict reliable 6D poses. Given that…

We consider distributed optimization under communication constraints for training deep learning models. We propose a new algorithm, whose parameter updates rely on two forces: a regular gradient step, and a corrective direction dictated by…

With the rapid development of Deep Learning, more and more applications on the cloud and edge tend to utilize large DNN (Deep Neural Network) models for improved task execution efficiency as well as decision-making quality. Due to memory…

We apply reduced-order modeling (ROM) techniques to single-phase flow in faulted porous media, accounting for changing rock properties and fault geometry variations using a radial basis function mesh deformation method. This approach…

This paper presents a deep learning-based de-homogenization method for structural compliance minimization. By using a convolutional neural network to parameterize the mapping from a set of lamination parameters on a coarse mesh to a…

Understanding the advantages of deep neural networks trained by gradient descent (GD) compared to shallow models remains an open theoretical challenge. In this paper, we introduce a class of target functions (single and multi-index Gaussian…

Memory replay based techniques have shown great success for continual learning with incrementally accumulated Euclidean data. Directly applying them to continually expanding networks, however, leads to the potential memory explosion problem…

We propose a Stochastic Gradient Descent (SGD)-type algorithm for Personalized Federated Learning which can be particularly attractive for mobile energy-limited regimes due to its low per-client computational cost. The model to be trained…

We propose a new iterative optimization method for the {\bf Data-Fitting} (DF) problem in Machine Learning, e.g. Neural Network (NN) training. The approach relies on {\bf Graphical Model} (GM) representation of the DF problem, where…

We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…

Although deep neural networks (NNs) have achievedstate-of-the-art accuracy in many visual recognition tasks,the growing computational complexity and energy con-sumption of networks remains an issue, especially for ap-plications on platforms…

Message passing on hypergraphs has been a standard framework for learning higher-order correlations between hypernodes. Recently-proposed hypergraph neural networks (HGNNs) can be categorized into spatial and spectral methods based on their…

The accurate representation of numerous physical, chemical, and biological processes relies heavily on differential equations (DEs), particularly nonlinear differential equations (NDEs). While understanding these complex systems…

During the last decades, many studies have been dedicated to improving the performance of neural networks, for example, the network architectures, initialization, and activation. However, investigating the importance and effects of…

The extreme learning machine (ELM) method can yield highly accurate solutions to linear/nonlinear partial differential equations (PDEs), but requires the last hidden layer of the neural network to be wide to achieve a high accuracy. If the…

With the ubiquitous graph-structured data in various applications, models that can learn compact but expressive vector representations of nodes have become highly desirable. Recently, bearing the message passing paradigm, graph neural…

We study a family of $H^m$-conforming piecewise polynomials based on artificial neural network, named as the finite neuron method (FNM), for numerical solution of $2m$-th order partial differential equations in $\mathbb{R}^d$ for any $m,d…

It has been shown that semi-parametric methods, which combine standard neural networks with non-parametric components such as external memory modules and data retrieval, are particularly helpful in data scarcity and out-of-distribution…

Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…