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Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…

In 2006, Geoffrey Hinton proposed the concept of training ''Deep Neural Networks (DNNs)'' and an improved model training method to break the bottleneck of neural network development. More recently, the introduction of AlphaGo in 2016…

This paper presents a novel approach for the output range estimation problem in Deep Neural Networks (DNNs) by integrating a Simulated Annealing (SA) algorithm tailored to operate within constrained domains and ensure convergence towards…

In scientific and engineering applications, solving partial differential equations (PDEs) across various parameters and domains normally relies on resource-intensive numerical methods. Neural operators based on deep learning offered a…

In this work, we introduce a machine/deep learning methodology to solve parametric integrals. Besides classical machine learning approaches, we consider a differential learning framework that incorporates derivative information during…

Deep neural networks (NNs) are powerful black box predictors that have recently achieved impressive performance on a wide spectrum of tasks. Quantifying predictive uncertainty in NNs is a challenging and yet unsolved problem. Bayesian NNs,…

We provide a general theory of the expectation-maximization (EM) algorithm for inferring high dimensional latent variable models. In particular, we make two contributions: (i) For parameter estimation, we propose a novel high dimensional EM…

For many practical problems and applications, it is not feasible to create a vast and accurately labeled dataset, which restricts the application of deep learning in many areas. Semi-supervised learning algorithms intend to improve…

We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the…

The ability to train Deep Neural Networks (DNNs) with constraints is instrumental in improving the fairness of modern machine-learning models. Many algorithms have been analysed in recent years, and yet there is no standard, widely accepted…

This paper proposes a domain decomposition subspace neural network method for efficiently solving linear and nonlinear partial differential equations. By combining the principles of domain decomposition and subspace neural networks, the…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

The recent decade has seen an enormous rise in the popularity of deep learning and neural networks. These algorithms have broken many previous records and achieved remarkable results. Their outstanding performance has significantly sped up…

We introduce semi-parametric inducing point networks (SPIN), a general-purpose architecture that can query the training set at inference time in a compute-efficient manner. Semi-parametric architectures are typically more compact than…

The image reconstruction process in medical imaging can be treated as solving an inverse problem. The inverse problem is usually solved using time-consuming iterative algorithms with sparsity or other constraints. Recently, deep neural…

Social network alignment, aligning different social networks on their common users, is receiving dramatic attention from both academic and industry. All existing studies consider the social network to be static and neglect its inherent…

In deep neural nets, lower level embedding layers account for a large portion of the total number of parameters. Tikhonov regularization, graph-based regularization, and hard parameter sharing are approaches that introduce explicit biases…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

The measured spatiotemporal response of various physical processes is utilized to infer the governing partial differential equations (PDEs). We propose SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE), a technique…

For the past couple of decades, numerical optimization has played a central role in addressing wireless resource management problems such as power control and beamformer design. However, optimization algorithms often entail considerable…