Related papers: Physics informed cell representations for variatio…

Physics-informed neural networks have shown significant potential in solving partial differential equations (PDEs) across diverse scientific fields. However, their performance often deteriorates when addressing PDEs with intricate and…

Deep learning methods have gained considerable interest in the numerical solution of various partial differential equations (PDEs). One particular focus is physics-informed neural networks (PINN), which integrate physical principles into…

Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…

Physics-informed neural networks (PINNs) have emerged as a promising mesh-free paradigm for solving partial differential equations, yet adoption in science and engineering is limited by slow training and modest accuracy relative to modern…

In this paper we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nano-optics technologies. In particular, we successfully…

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…

Although physics-informed neural networks(PINNs) have progressed a lot in many real applications recently, there remains problems to be further studied, such as achieving more accurate results, taking less training time, and quantifying the…

This paper advances the use of physics-informed neural networks (PINNs) architectures to address moving interface problems via the level set method. Originally developed for other PDE-based problems, we particularly leverage PirateNet's…

Physics-informed neural networks (PINNs) have emerged as a powerful approach for solving partial differential equations (PDEs) by training neural networks with loss functions that incorporate physical constraints. In this work, we introduce…

Physics Informed Neural Networks (PINNs) have been emerging as a powerful computational tool for solving differential equations. However, the applicability of these models is still in its initial stages and requires more standardization to…

Partial differential equations (PDEs) on surfaces are fundamental to scientific computing and geometry processing. A popular approach to solving PDEs on surfaces is the finite element method (FEM), where the surface is divided into discrete…

Multi-level methods are widely used for the solution of large-scale problems, because of their computational advantages and exploitation of the complementarity between the involved sub-problems. After a re-interpretation of multi-level…

In this study, we explore the application of Physics-Informed Neural Networks (PINNs) to the analysis of bifurcation phenomena in ecological migration models. By integrating the fundamental principles of diffusion-advection-reaction…

Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to…

This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms…

I present a simple hybrid framework that combines physics informed neural networks (PINNs) with features generated from small quantum circuits. As a proof of concept, a first-order equation is solved by feeding quantum measurement…

In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solution for partial differential equations (PDEs) in case of arbitrary geometries while strictly enforcing…

Solving analytically intractable partial differential equations (PDEs) that involve at least one variable defined on an unbounded domain arises in numerous physical applications. Accurately solving unbounded domain PDEs requires efficient…

We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the…

In this study, we introduce a method based on Separable Physics-Informed Neural Networks (SPINNs) for effectively solving the BGK model of the Boltzmann equation. While the mesh-free nature of PINNs offers significant advantages in handling…