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We proposed a simple yet effective morphological approach to convert a sparse Digital Elevation Model (DEM) to a dense Digital Elevation Model. The conversion is similar to that of the generation of high-resolution DEM from its…
Motivated by renal imaging studies that combine renogram curves with pharmacokinetic and demographic covariates, we propose Hybrid partial least squares (Hybrid PLS) for simultaneous supervised dimension reduction and regression in the…
We propose a least-squares method involving the recovery of the gradient and possibly the Hessian for elliptic equation in nondivergence form. As our approach is based on the Lax--Milgram theorem with the curl-free constraint built into the…
Residual neural networks (ResNets) are a promising class of deep neural networks that have shown excellent performance for a number of learning tasks, e.g., image classification and recognition. Mathematically, ResNet architectures can be…
This paper deals with sparse feature selection and grouping for classification and regression. The classification or regression problems under consideration consists in minimizing a convex empirical risk function subject to an $\ell^1$…
We propose a hybrid physics-informed framework for solving families of parametric linear partial differential equations (PDEs) by combining a meta-learned predictor with a least-squares corrector. The predictor, termed \textbf{KAPI}…
Convolutional neural networks (CNNs) have developed to become powerful models for various computer vision tasks ranging from object detection to semantic segmentation. However, most of the state-of-the-art CNNs cannot be deployed directly…
Extreme learning machines (ELMs), which preset hidden layer parameters and solve for last layer coefficients via a least squares method, can typically solve partial differential equations faster and more accurately than Physics Informed…
Communication compression has become a key strategy to speed up distributed optimization. However, existing decentralized algorithms with compression mainly focus on compressing DGD-type algorithms. They are unsatisfactory in terms of…
In this paper, we develop a new optimization framework for the least squares learning problem via fully connected neural networks or physics-informed neural networks. The gradient descent sometimes behaves inefficiently in deep learning…
Adversarial training can be used to learn models that are robust against perturbations. For linear models, it can be formulated as a convex optimization problem. Compared to methods proposed in the context of deep learning, leveraging the…
Parallelization framework has become a necessity to speed up the training of deep neural networks (DNN) recently. Such framework typically employs the Model Average approach, denoted as MA-DNN, in which parallel workers conduct respective…
Distributed optimization methods are often applied to solving huge-scale problems like training neural networks with millions and even billions of parameters. In such applications, communicating full vectors, e.g., (stochastic) gradients,…
In the last decade, Convolutional Neural Network with a multi-layer architecture has advanced rapidly. However, training its complex network is very space-consuming, since a lot of intermediate data are preserved across layers, especially…
Recent years have witnessed the great advance of deep learning in a variety of vision tasks. Many state-of-the-art deep neural networks suffer from large size and high complexity, which makes it difficult to deploy in resource-limited…
Artificial Intelligence algorithms have been steadily increasing in popularity and usage. Deep Learning, allows neural networks to be trained using huge datasets and also removes the need for human extracted features, as it automates the…
Deep Evolutionary Network Structured Representation (DENSER) is a novel approach to automatically design Artificial Neural Networks (ANNs) using Evolutionary Computation. The algorithm not only searches for the best network topology (e.g.,…
In presence of sparse noise we propose kernel regression for predicting output vectors which are smooth over a given graph. Sparse noise models the training outputs being corrupted either with missing samples or large perturbations. The…
We consider hyperelastic problems and their numerical solution using a conforming finite element discretization and iterative linearization algorithms. For these problems, we present equilibrated, weakly symmetric, $H(\rm{div)}$-conforming…
The iteratively reweighted least squares method (IRLS) is a popular technique used in practice for solving regression problems. Various versions of this method have been proposed, but their theoretical analyses failed to capture the good…