English
Related papers

Related papers: Approximating electromagnetic fields in discontinu…

200 papers

Despite the remarkable progress of physics-informed neural networks (PINNs) in scientific computing, they continue to face challenges when solving hydrodynamic problems with multiple discontinuities. In this work, we propose…

Fluid Dynamics · Physics 2025-05-28 Chuanxing Wang , Hui Luo , Kai Wang , Guohuai Zhu , Mingxing Luo

Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft…

Machine Learning · Computer Science 2022-12-09 Rambod Mojgani , Maciej Balajewicz , Pedram Hassanzadeh

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

Numerical Analysis · Mathematics 2020-06-16 Chengping Rao , Hao Sun , Yang Liu

Physics-informed neural networks (PINNs) have demonstrated promise as a framework for solving forward and inverse problems involving partial differential equations. Despite recent progress in the field, it remains challenging to quantify…

Machine Learning · Computer Science 2025-11-14 Bruno Jacob , Ashish S. Nair , Amanda A. Howard , Jan Drgona , Panos Stinis

The solution of partial differential equations (PDES) on irregular domains has long been a subject of significant research interest. In this work, we present an approach utilizing physics-informed neural networks (PINNs) to achieve…

Computational Physics · Physics 2025-06-12 Cuizhi Zhou , Kaien Zhu

There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Networks (PINNs). In this paper, we develop Physics Informed…

Machine Learning · Computer Science 2019-07-09 Vikas Dwivedi , Balaji Srinivasan

This research explores neural network-based numerical approximation of two-dimensional convection-dominated singularly perturbed problems on square, circular, and elliptic domains. Singularly perturbed boundary value problems pose…

Numerical Analysis · Mathematics 2024-07-11 Gung-Min Gie , Youngjoon Hong , Chang-Yeol Jung , Dongseok Lee

The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power…

Systems and Control · Electrical Eng. & Systems 2023-11-13 Jochen Stiasny , Spyros Chatzivasileiadis

Physics-informed neural networks (PINNs) hold the potential for supplementing the existing set of techniques for solving differential equations that emerge in the study of black hole quasinormal modes. The present research investigated them…

General Relativity and Quantum Cosmology · Physics 2021-08-13 Anele M Ncube , Gerhard E Harmsen , Alan S Cornell

Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating…

Fluid Dynamics · Physics 2024-07-12 Shengfeng Xu , Chang Yan , Zhenxu Sun , Renfang Huang , Dilong Guo , Guowei Yang

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…

Numerical Analysis · Mathematics 2024-07-30 Hamed Saidaoui , Luis Espath , Rául Tempone

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…

Machine Learning · Computer Science 2024-08-20 Woojin Cho , Minju Jo , Haksoo Lim , Kookjin Lee , Dongeun Lee , Sanghyun Hong , Noseong Park

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…

Numerical Analysis · Mathematics 2024-11-28 Marco Berardi , Fabio Difonzo , Matteo Icardi

Physics-informed neural networks (PINNs) are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly…

Computational Physics · Physics 2021-11-03 Guofei Pang , Lu Lu , George Em Karniadakis

Physics-Informed Neural Networks (PINNs) have recently emerged as a novel approach to simulate complex physical systems on the basis of both data observations and physical models. In this work, we investigate the use of PINNs for various…

Analysis of PDEs · Mathematics 2024-03-27 Guillaume Coulaud , Maxime Le , Régis Duvigneau

The present work investigates the use of physics-informed neural networks (PINNs) for the 3D reconstruction of unsteady gravity currents from limited data. In the PINN context, the flow fields are reconstructed by training a neural network…

Fluid Dynamics · Physics 2023-06-16 Mickaël Delcey , Yoann Cheny , Sébastien Kiesgen de Richter

Physics informed neural networks (PINNs) require regularity of solutions of the underlying PDE to guarantee accurate approximation. Consequently, they may fail at approximating discontinuous solutions of PDEs such as nonlinear hyperbolic…

Numerical Analysis · Mathematics 2022-07-19 Tim De Ryck , Siddhartha Mishra , Roberto Molinaro

In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate…

Numerical Analysis · Mathematics 2025-08-12 Feng Han , Jianguo Wang , Guoliang Peng , Xueting Shi

This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are…

Machine Learning · Computer Science 2023-09-26 Taniya Kapoor , Hongrui Wang , Alfredo Nunez , Rolf Dollevoet

Physics-Informed Neural Networks (PINNs) solve forward PDEs by minimizing residual losses from the governing equations with initial and boundary conditions, but they often struggle with discontinuities such as shocks. In contrast, finite…

Fluid Dynamics · Physics 2026-02-05 Yeping Wang , Shihao Yang