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Regression with non-Euclidean responses -- e.g., probability distributions, networks, symmetric positive-definite matrices, and compositions -- has become increasingly important in modern applications. In this paper, we propose deep…

In time-varying fading channels, channel coefficients are estimated using pilot symbols that are transmitted every coherence interval. For channels with high Doppler spread, the rapid channel variations over time will require considerable…

Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…

This paper establishes statistical properties of deep neural network (DNN) estimators under dependent data. Two general results for nonparametric sieve estimators directly applicable to DNN estimators are given. The first establishes rates…

Deep neural networks (DNN) with a huge number of adjustable parameters remain largely black boxes. To shed light on the hidden layers of DNN, we study supervised learning by a DNN of width $N$ and depth $L$ consisting of $NL$ perceptrons…

Deep Neural Networks (DNNs) are rapidly being applied to safety-critical domains such as drone and airplane control, motivating techniques for verifying the safety of their behavior. Unfortunately, DNN verification is NP-hard, with current…

The attenuation of acoustic loudspeaker echoes remains to be one of the open challenges to achieve pleasant full-duplex hands free speech communication. In many modern signal enhancement interfaces, this problem is addressed by a linear…

The inverse scattering problem is of critical importance in a number of fields, including medical imaging, sonar, sensing, non-destructive evaluation, and several others. The problem of interest can vary from detecting the shape to the…

We consider the numerical solution of an acoustic scattering problem by the Plane Wave Discontinuous Galerkin Method (PWDG) in the exterior of a bounded domain in $\mathbb{R}^2$. In order to apply the PWDG method, we introduce an artificial…

We studied the use of deep neural networks (DNNs) in the numerical solution of the oscillatory Fredholm integral equation of the second kind. It is known that the solution of the equation exhibits certain oscillatory behaviors due to the…

Whereas recovery of the manifold from data is a well-studied topic, approximation rates for functions defined on manifolds are less known. In this work, we study a regression problem with inputs on a $d^*$-dimensional manifold that is…

This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to…

We investigate methods for experimental performance enhancement of auto-encoders based on a recurrent neural network (RNN) for communication over dispersive nonlinear channels. In particular, our focus is on the recently proposed sliding…

In the Coded Aperture Snapshot Spectral Imaging (CASSI) system, deep unfolding networks (DUNs) have demonstrated excellent performance in recovering 3D hyperspectral images (HSIs) from 2D measurements. However, some noticeable gaps exist…

Deep neural networks (NN) are extensively used for machine learning tasks such as image classification, perception and control of autonomous systems. Increasingly, these deep NNs are also been deployed in high-assurance applications. Thus,…

This paper presents a virtual boundary integral neural network (VBINN) for exterior acoustic problems in three dimensions. The method introduces a virtual boundary inside the scatterer or vibrating body and represents the associated source…

Full-Waveform Inversion seeks to achieve a high-resolution model of the subsurface through the application of multi-variate optimization to the seismic inverse problem. Although now a mature technology, FWI has limitations related to the…

We propose a novel deep neural network (DNN) based approximation architecture to learn estimates of measurements. We detail an algorithm that enables training of the DNN. The DNN estimator only uses measurements, if and when they are…

Subjective evaluation results for two low-latency deep neural networks (DNN) are compared to a matured version of a traditional Wiener-filter based noise suppressor. The target use-case is real-world single-channel speech enhancement…

We study the approximation capacity of deep ReLU recurrent neural networks (RNNs) and explore the convergence properties of nonparametric least squares regression using RNNs. We derive upper bounds on the approximation error of RNNs for…