Related papers: Deep ReLU Neural Network Emulation in High-Frequen…
Deep Neural Networks (DNN) have been successful in en- hancing noisy speech signals. Enhancement is achieved by learning a nonlinear mapping function from the features of the corrupted speech signal to that of the reference clean speech…
We present a comprehensive framework for deriving rigorous and efficient bounds on the approximation error of deep neural networks in PDE models characterized by branching mechanisms, such as waves, Schr\"odinger equations, and other…
A neural network is essentially a high-dimensional complex mapping model by adjusting network weights for feature fitting. However, the spectral bias in network training leads to unbearable training epochs for fitting the high-frequency…
Ensuring solution feasibility is a key challenge in developing Deep Neural Network (DNN) schemes for solving constrained optimization problems, due to inherent DNN prediction errors. In this paper, we propose a ``preventive learning''…
Using deep neural networks to solve PDEs has attracted a lot of attentions recently. However, why the deep learning method works is falling far behind its empirical success. In this paper, we provide a rigorous numerical analysis on deep…
Neural networks have emerged as a tool for solving differential equations in many branches of engineering and science. But their progress in frequency domain acoustics is limited by the vanishing gradient problem that occurs at higher…
Recently, several deep learning (DL) methods for approximating high-dimensional partial differential equations (PDEs) have been proposed. The interest that these methods have generated in the literature is in large part due to simulations…
We studied the ability of deep neural networks (DNNs) to restore missing audio content based on its context, a process usually referred to as audio inpainting. We focused on gaps in the range of tens of milliseconds. The proposed DNN…
Consider a time-harmonic acoustic plane wave incident onto an elastic body with an unbounded periodic surface. The medium above the surface is supposed to be filled with a homogeneous compressible inviscid air/fluid of constant mass…
This paper presents a novel machine-hearing system that exploits deep neural networks (DNNs) and head movements for robust binaural localisation of multiple sources in reverberant environments. DNNs are used to learn the relationship…
In this paper, we present a method that allows to further improve speech enhancement obtained with recently introduced Deep Neural Network (DNN) models. We propose a multi-channel refinement method of time-frequency masks obtained with…
In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in…
Analytical phase demodulation algorithms in optical interferometry typically fail to reach the theoretical sensitivity limit set by the Cram\'er-Rao bound (CRB). We show that deep neural networks (DNNs) can perform efficient phase…
The success of deep learning has inspired recent interests in applying neural networks in statistical inference. In this paper, we investigate the use of deep neural networks for nonparametric regression with measurement errors. We propose…
We present a novel deep Recurrent Neural Network (RNN) model for acoustic modelling in Automatic Speech Recognition (ASR). We term our contribution as a TC-DNN-BLSTM-DNN model, the model combines a Deep Neural Network (DNN) with Time…
We study the approximation of the median of $d$ inputs using ReLU neural networks. We present depth-width tradeoffs under several settings, culminating in a constant-depth, linear-width construction that achieves exponentially small…
This paper is devoted to a novel quantitative imaging scheme of identifying impenetrable obstacles in time-harmonic acoustic scattering from the associated far-field data. The proposed method consists of two phases. In the first phase, we…
Nonlinear differential equations are challenging to solve numerically and are important to understanding the dynamics of many physical systems. Deep neural networks have been applied to help alleviate the computational cost that is…
Spectral mapping uses a deep neural network (DNN) to map directly from noisy speech to clean speech. Our previous study found that the performance of spectral mapping improves greatly when using helpful cues from an acoustic model trained…
Deep neural networks (DNNs) have emerged as a powerful tool with a growing body of literature exploring Lyapunov-based approaches for real-time system identification and control. These methods depend on establishing bounds for the second…