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A serious concern for semi-analytical galaxy formation models, aiming to simulate multi-wavelength surveys and to thoroughly explore the model parameter space, is the extremely time consuming numerical solution of the radiative transfer of…
Partial differential equations (PDEs) provide a mathematical foundation for simulating and understanding intricate behaviors in both physical sciences and engineering. With the growing capabilities of deep learning, data$-$driven approaches…
Physics-Informed Neural Network (PINN) has proven itself a powerful tool to obtain the numerical solutions of nonlinear partial differential equations (PDEs) leveraging the expressivity of deep neural networks and the computing power of…
Recurrent neural networks (RNNs) hold immense potential for computations due to their Turing completeness and sequential processing capabilities, yet existing methods for their training encounter efficiency challenges. Backpropagation…
Graph neural network (GNN) is a promising approach to learning and predicting physical phenomena described in boundary value problems, such as partial differential equations (PDEs) with boundary conditions. However, existing models…
Physics-informed neural network (PINN) has shown great potential in solving partial differential equations. However, it faces challenges when dealing with problems involving steep gradients. The solutions to singularly perturbed…
Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…
Deep learning has recently emerged as a disruptive technology to solve challenging radio resource management problems in wireless networks. However, the neural network architectures adopted by existing works suffer from poor scalability,…
Multi-frequency Electrical Impedance Tomography (mfEIT) represents a promising biomedical imaging modality that enables the estimation of tissue conductivities across a range of frequencies. Addressing this challenge, we present a novel…
When investigating epidemic dynamics through differential models, the parameters needed to understand the phenomenon and to simulate forecast scenarios require a delicate calibration phase, often made even more challenging by the scarcity…
Graph processes exhibit a temporal structure determined by the sequence index and and a spatial structure determined by the graph support. To learn from graph processes, an information processing architecture must then be able to exploit…
Utilizing machine learning to address partial differential equations (PDEs) presents significant challenges due to the diversity of spatial domains and their corresponding state configurations, which complicates the task of encompassing all…
Thermal radiative transfer (TRT) is an essential piece of physics in inertial confinement fusion, high-energy density physics, astrophysics etc. The physical models of this type of problem are defined by strongly coupled differential…
Photonic neural networks (PNNs) are fast in-propagation and high bandwidth paradigms that aim to popularize reproducible NN acceleration with higher efficiency and lower cost. However, the training of PNN is known to be challenging, where…
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…
A common problem in training neural networks is the vanishing and/or exploding gradient problem which is more prominently seen in training of Recurrent Neural Networks (RNNs). Thus several algorithms have been proposed for training RNNs.…
The neutron diffusion equation plays a pivotal role in the analysis of nuclear reactors. Nevertheless, employing the Physics-Informed Neural Network (PINN) method for its solution entails certain limitations. Traditional PINN approaches…
This study analyzes Graph Neural Networks (GNNs) for distribution system state estimation (DSSE) by employing an interpretable Graph Neural Additive Network (GNAN) and by utilizing an edge-conditioned message-passing mechanism. The…
The incompressible magnetohydrodynamic (MHD) equations are fundamental in many scientific and engineering applications. However, their strong nonlinearity and dual divergence-free constraints make them highly challenging for conventional…
This paper presents $\Psi$-GNN, a novel Graph Neural Network (GNN) approach for solving the ubiquitous Poisson PDE problems with mixed boundary conditions. By leveraging the Implicit Layer Theory, $\Psi$-GNN models an "infinitely" deep…