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Input-Convex Neural Networks (ICNNs) are networks that guarantee convexity in their input-output mapping. These networks have been successfully applied for energy-based modelling, optimal transport problems and learning invariances. The…

Solutions to differential equations are of significant scientific and engineering relevance. Recently, there has been a growing interest in solving differential equations with neural networks. This work develops a novel method for solving…

Deep Neural Networks (DNNs) have demonstrated remarkable success across a wide range of tasks, particularly in fields such as image classification. However, DNNs are highly susceptible to adversarial attacks, where subtle perturbations are…

We propose a first-order method for solving inequality constrained optimization problems. The method is derived from our previous work [12], a modified search direction method (MSDM) that applies the singular-value decomposition of…

Monocular depth estimation is an extensively studied computer vision problem with a vast variety of applications. Deep learning-based methods have demonstrated promise for both supervised and unsupervised depth estimation from monocular…

The study of parametric differential equations plays a crucial role in weather forecasting and epidemiological modeling. These phenomena are better represented using fractional derivatives due to their inherent memory or hereditary effects.…

Detecting and localizing leakages is a significant challenge for the efficient and sustainable management of water distribution networks (WDN). Leveraging the inherent graph structure of WDNs, recent approaches have used graph-based…

Algebraic multigrid (AMG) methods are among the most efficient solvers for linear systems of equations and they are widely used for the solution of problems stemming from the discretization of Partial Differential Equations (PDEs). The most…

Efficiently solving the Fokker-Planck equation (FPE) is central to analyzing complex parameterized stochastic systems. However, current numerical methods lack parallel computation capabilities across varying conditions, severely limiting…

Deep neural networks often suffer from poor performance or even training failure due to the ill-conditioned problem, the vanishing/exploding gradient problem, and the saddle point problem. In this paper, a novel method by acting the…

We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity…

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

We develop a deep learning approach to extract ray directions at discrete locations by analyzing highly oscillatory wave fields. A deep neural network is trained on a set of local plane-wave fields to predict ray directions at discrete…

We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN,…

Singularly perturbed dynamical systems play a crucial role in climate dynamics and plasma physics. A powerful and well-known tool to address these systems is the Fenichel normal form, which significantly simplifies fast dynamics near slow…

In recent years, even though Stochastic Gradient Descent (SGD) and its variants are well-known for training neural networks, it suffers from limitations such as the lack of theoretical guarantees, vanishing gradients, and excessive…

We extend and analyze the deep neural network multigrid solver (DNN-MG) for the Navier-Stokes equations in three dimensions. The idea of the method is to augment a finite element simulation on coarse grids with fine scale information…

Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and…

Recently, message-passing graph neural networks (MPNNs) have shown potential for solving combinatorial and continuous optimization problems due to their ability to capture variable-constraint interactions. While existing approaches leverage…

We design and successfully implement artificial neural networks (ANNs) to detect and classify entanglement for three-qubit systems using limited state features. The overall design principle is a feed forward neural network (FFNN), with the…