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Deep neural networks (DNNs) offer a real-time solution for the inversion of borehole resistivity measurements to approximate forward and inverse operators. It is possible to use extremely large DNNs to approximate the operators, but it…

The remarkable performance of deep neural networks (DNNs) currently makes them the method of choice for solving linear inverse problems. They have been applied to super-resolve and restore images, as well as to reconstruct MR and CT images.…

On account of its many successes in inference tasks and denoising applications, Dictionary Learning (DL) and its related sparse optimization problems have garnered a lot of research interest. While most solutions have focused on single…

We introduce a new second-order inertial optimization method for machine learning called INNA. It exploits the geometry of the loss function while only requiring stochastic approximations of the function values and the generalized…

As a method of universal approximation deep neural networks (DNNs) are capable of finding approximate solutions to problems posed with little more constraints than a suitably-posed mathematical system and an objective function.…

Neural ordinary differential equations (NODEs) treat computation of intermediate feature vectors as trajectories of ordinary differential equation parameterized by a neural network. In this paper, we propose a novel model, delay…

Numerical solution of partial differential equations (PDEs) plays a vital role in various fields of science and engineering. In recent years, deep neural networks (DNNs) have emerged as a powerful tool for solving PDEs, leveraging their…

The increasing use of deep neural networks (DNNs) in safety-critical systems has raised concerns about their potential for exhibiting ill-behaviors. While DNN verification and testing provide post hoc conclusions regarding unexpected…

Deep neural networks (DNNs) have been used to model complex optimization problems in many applications, yet have difficulty guaranteeing solution optimality and feasibility, despite training on large datasets. Training a NN as a surrogate…

Deep neural network (DNN) regression models are widely used in applications requiring state-of-the-art predictive accuracy. However, until recently there has been little work on accurate uncertainty quantification for predictions from such…

Deep neural networks (DNNs) provide useful models of visual representational transformations. We present a method that enables a DNN (student) to learn from the internal representational spaces of a reference model (teacher), which could be…

In the present work a new set of differential equations for the Hopfield Neural Network (HNN) method were established by means of the Linear Extended Gateaux Derivative (LEGD). This new approach will be referred to as G\^ateaux-Hopfiel…

Understanding deep learning is increasingly emergent as it penetrates more and more into industry and science. In recent years, a research line from Fourier analysis sheds lights on this magical "black box" by showing a Frequency Principle…

A filtered density function (FDF) model based on deep neural network (DNN), termed DNN-FDF, is introduced for large eddy simulation (LES) of turbulent flows involving conserved scalar transport. The primary objectives of this study are to…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

Deep Neural Networks (DNNs) are typically trained by backpropagation in a batch learning setting, which requires the entire training data to be made available prior to the learning task. This is not scalable for many real-world scenarios…

In this study, we prove rigourous bounds on the error and stability analysis of deep learning methods for the nonstationary Magneto-hydrodynamics equations. We obtain the approximate ability of the neural network by the convergence of a…

Geometric Deep Learning (GDL) unifies a broad class of machine learning techniques from the perspectives of symmetries, offering a framework for introducing problem-specific inductive biases like Graph Neural Networks (GNNs). However, the…

Significance: Optical neuroimaging has become a well-established clinical and research tool to monitor cortical activations in the human brain. It is notable that outcomes of functional Near-InfraRed Spectroscopy (fNIRS) studies depend…

This paper presents an efficient spectral method for solving the fractional Fredholm integro-differential equations. The non-smoothness of the solutions to such problems leads to the performance of spectral methods based on the classical…