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Physics-Informed Neural Networks (PINNs) embed the partial differential equations (PDEs) governing the system under study directly into the training of Neural Networks, ensuring solutions that respect physical laws. While effective for…

Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence…

We present the asymptotic transitions from microscopic to macroscopic physics, their computational challenges and the Asymptotic-Preserving (AP) strategies to efficiently compute multiscale physical problems. Specifically, we will first…

Physics-informed neural networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…

Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…

Graph neural networks (GNNs), and especially message-passing neural networks, excel in various domains such as physics, drug discovery, and molecular modeling. The expressivity of GNNs with respect to their ability to discriminate…

Graph Neural Networks (GNNs) have emerged as a powerful tool for learning on graph-structured data, finding applications in numerous domains including social network analysis and molecular biology. Within this broad category, Asynchronous…

In this paper, a modified version of conservative Physics-informed Neural Networks (cPINN for short) is provided to construct the weak solutions of Riemann problem for the hyperbolic scalar conservation laws in non-conservative form. To…

Standard Physics-Informed Neural Networks (PINNs) often face challenges when modeling parameterized dynamical systems with sharp regime transitions, such as bifurcations. In these scenarios, the continuous mapping from parameters to…

Weight pruning methods for deep neural networks (DNNs) have been investigated recently, but prior work in this area is mainly heuristic, iterative pruning, thereby lacking guarantees on the weight reduction ratio and convergence time. To…

We propose Weak and Entropy PINNs (WE-PINNs) for the approximation of entropy solutions to nonlinear hyperbolic conservation laws. Standard physics-informed neural networks enforce governing equations in strong differential form, an…

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 work addresses the accurate and efficient simulation of physical phenomena governed by parametric Partial Differential Equations (PDEs) characterized by varying boundary conditions, where parametric instances modify not only the…

The analogy to heat diffusion has enhanced our understanding of information flow in graphs and inspired the development of Graph Neural Networks (GNNs). However, most diffusion-based GNNs emulate passive heat diffusion, which still suffers…

With the improvement of the pattern recognition and feature extraction of Deep Neural Networks (DPNNs), image-based design and optimization have been widely used in multidisciplinary researches. Recently, a Reconstructive Neural Network…

Physics-Informed Neural Networks (PINNs) offer a flexible framework for solving nonlinear partial differential equations (PDEs), yet conventional implementations often fail to preserve key physical invariants during long-term integration.…

The gravitational collapse of a massless scalar field remains a demanding benchmark for numerical methods in numerical relativity, as it exhibits critical behavior at the boundary between dispersion and black hole formation. In this work we…

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…

Radio-Frequency (RF) imaging concerns the digital recreation of the surfaces of scene objects based on the scattered field at distributed receivers. To solve this difficult inverse scattering problems, data-driven methods are often employed…

We introduce a hybrid "Modified Genetic Algorithm-Multilevel Stochastic Gradient Descent" (MGA-MSGD) training algorithm that considerably improves accuracy and efficiency of solving 3D mechanical problems described, in strong-form, by PDEs…