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Pointer Network (PtrNet) is a specific neural network for solving Combinatorial Optimization Problems (COPs). While PtrNets offer real-time feed-forward inference for complex COPs instances, its quality of the results tends to be less…

We study the problem of asymptotic consensus as it occurs in a wide range of applications in both man-made and natural systems. In particular, we study systems with directed communication graphs that may change over time. We recently…

Deep neural networks (DNNs) are highly susceptible to adversarial examples--subtle perturbations applied to inputs that are often imperceptible to humans yet lead to incorrect model predictions. In black-box scenarios, however, existing…

Purpose: Neural networks have received recent interest for reconstruction of undersampled MR acquisitions. Ideally network performance should be optimized by drawing the training and testing data from the same domain. In practice, however,…

Mesh-based Graph Neural Networks (GNNs) have recently shown capabilities to simulate complex multiphysics problems with accelerated performance times. However, mesh-based GNNs require a large number of message-passing (MP) steps and suffer…

The Gray Radiative Transfer Equations (GRTEs) are high-dimensional, multiscale problems that pose significant computational challenges for traditional numerical methods. Current deep learning approaches, including Physics-Informed Neural…

In this paper, we develop and employ auxiliary physics-informed neural networks (APINNs) to solve forward, inverse, and coupled integro-differential problems of radiative transfer theory (RTE). Specifically, by focusing on the relevant slab…

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

This paper deals with the boundary value problems for the singularly perturbed differential-algebraic system of equations. The case of turning points has been studied. The sufficient conditions for existence and uniqueness of the solution…

The self-consistent expansion (SCE) is a powerful technique for obtaining perturbative solutions to problems in statistical physics but it suffers from a subtle problem - too much freedom! The SCE can be used to generate an enormous number…

Mathematical formulas serve as the means of communication between humans and nature, encapsulating the operational laws governing natural phenomena. The concise formulation of these laws is a crucial objective in scientific research and an…

Considering deep neural networks as manifold mappers, the pretrain-then-fine-tune paradigm can be interpreted as a two-stage process: pretrain establishes a broad knowledge base, and fine-tune adjusts the model parameters to activate…

Machine learning methods for solving nonlinear partial differential equations (PDEs) are hot topical issues, and different algorithms proposed in the literature show efficient numerical approximation in high dimension. In this paper, we…

This work is focused on the modelling of signal propagations in myelinated axons to characterize the functions of the myelin sheath in the neural structure. Based on reasonable assumptions on the medium properties, we derive a…

In this article, our goal is to solve two-parameter singular perturbation problems (SPPs) in one- and two-dimensions using an adapted Physics-Informed Neural Networks (PINNs) approach. Such problems are of major importance in engineering…

We propose a method combining boundary integral equations and neural networks (BINet) to solve partial differential equations (PDEs) in both bounded and unbounded domains. Unlike existing solutions that directly operate over original PDEs,…

This paper introduces a novel type of memetic algorithm based Topology and Weight Evolving Artificial Neural Network (TWEANN) system called DX Neural Network (DXNN). DXNN implements a number of interesting features, amongst which is: a…

In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of…

The rapid progress in 6G communication and high-bandwidth radar has driven an unprecedented surge in the spatial density of signal sources, resulting in an increasingly congested electromagnetic (EM) environment. When resolving closely…

Deep learning models tend to underperform in the presence of domain shifts. Domain transfer has recently emerged as a promising approach wherein images exhibiting a domain shift are transformed into other domains for augmentation or…