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The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…

A nonlinear Schr\"odinger equation (NLS) on a periodic box can be discretized as a discrete nonlinear Schr\"odinger equation (DNLS) on a periodic cubic lattice, which is a system of finitely many ordinary differential equations. We show…

An important problem in fiber-optic communications is to invert the nonlinear Schr\"odinger equation in real time to reverse the deterministic effects of the channel. Interestingly, the popular split-step Fourier method (SSFM) leads to a…

The memorization effect of deep neural networks (DNNs) plays a pivotal role in recent label noise learning methods. To exploit this effect, the model prediction-based methods have been widely adopted, which aim to exploit the outputs of…

The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…

Accurately estimating parameters in complex nonlinear systems is crucial across scientific and engineering fields. We present a novel approach for parameter estimation using a neural network with the Huber loss function. This method taps…

Federated learning (FL) is an emerging paradigm for decentralized training of machine learning models on distributed clients, without revealing the data to the central server. The learning scheme may be horizontal, vertical or hybrid (both…

Federated Learning (FL) is a distributed learning technique that maintains data privacy by providing a decentralized training method for machine learning models using distributed big data. This promising Federated Learning approach has also…

Robust local feature representations are essential for spatial intelligence tasks such as robot navigation and augmented reality. Establishing reliable correspondences requires descriptors that provide both high discriminative power and…

In this paper, we introduce a Deep Neural Network (DNN) to maximize the Proportional Fairness (PF) of the Spectral Efficiency (SE) of uplinks in Cell-Free (CF) massive Multiple-Input Multiple-Output (MIMO) systems. The problem of maximizing…

Federated Learning (FL) is designed as a decentralized, privacy-preserving machine learning paradigm that enables multiple clients to collaboratively train a model without sharing their data. In real-world scenarios, however, clients often…

Federated Learning (FL) is a framework which enables distributed model training using a large corpus of decentralized training data. Existing methods aggregate models disregarding their internal representations, which are crucial for…

In this paper we present a Fourier feature based deep domain decomposition method (F-D3M) for partial differential equations (PDEs). Currently, deep neural network based methods are actively developed for solving PDEs, but their efficiency…

Deep neural networks (DNNs) have achieved exceptional performance across various fields by learning complex, nonlinear mappings from large-scale datasets. However, they face challenges such as high memory requirements and computational…

Deep neural networks (DNNs) have achieved significant success across various tasks, but ensuring reliable uncertainty estimates, known as model calibration, is crucial for their safe and effective deployment. Modern DNNs often suffer from…

Uncertainty is a fundamental aspect of real-world scenarios, where perfect information is rarely available. Humans naturally develop complex internal models to navigate incomplete data and effectively respond to unforeseen or partially…

Recently convolutional neural networks (CNNs) achieve great accuracy in visual recognition tasks. DenseNet becomes one of the most popular CNN models due to its effectiveness in feature-reuse. However, like other CNN models, DenseNets also…

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…

In recent years, deep metric learning has achieved promising results in learning high dimensional semantic feature embeddings where the spatial relationships of the feature vectors match the visual similarities of the images. Similarity…

We propose a method for integration of features extracted using deep representations of Convolutional Neural Networks (CNNs) each of which is learned using a different image dataset of objects and materials for material recognition. Given a…