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This study compares the Boundary Element Method (BEM) and Physics-Informed Neural Networks (PINNs) for solving the two-dimensional Helmholtz equation in wave scattering problems. The objective is to evaluate the performance of both methods…

Physics-informed neural networks (PINN) have been widely used in computational physics to solve partial differential equations (PDEs). In this study, we propose an energy-embedding-based physics-informed neural network method for solving…

Computational Physics · Physics 2025-06-02 Yi-Qiang Wu , Xuan Liu , Hanlin Li , Fuqiang Wang

The great success of Physics-Informed Neural Networks (PINN) in solving partial differential equations (PDEs) has significantly advanced our simulation and understanding of complex physical systems in science and engineering. However, many…

Numerical Analysis · Mathematics 2024-09-10 Hao Zhang , Longxiang Jiang , Xinkun Chu , Yong Wen , Luxiong Li , Yonghao Xiao , Liyuan Wang

The accurate determination of electron properties is fundamental to low-temperature plasma simulations, necessitating precise solutions to the spatially inhomogeneous electron Boltzmann equation (EBE). This work explores the use of…

Plasma Physics · Physics 2026-05-07 Ihda Chaerony Siffa , Detlef Loffhagen , Markus M. Becker , Jan Trieschmann

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) are a versatile tool in the burgeoning field of scientific machine learning for solving partial differential equations (PDEs). However, determining suitable training strategies for them is not…

Numerical Analysis · Mathematics 2026-03-09 Saad Qadeer , Panos Stinis

Eigenvalue problems are critical to several fields of science and engineering. We expand on the method of using unsupervised neural networks for discovering eigenfunctions and eigenvalues for differential eigenvalue problems. The obtained…

Machine Learning · Computer Science 2022-03-02 Henry Jin , Marios Mattheakis , Pavlos Protopapas

Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing…

Machine Learning · Computer Science 2024-12-11 Arturo Rodriguez , Ashesh Chattopadhyay , Piyush Kumar , Luis F. Rodriguez , Vinod Kumar

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…

Machine Learning · Computer Science 2024-09-18 Shivprasad Kathane , Shyamprasad Karagadde

Physics informed neural network (PINN) based solution methods for differential equations have recently shown success in a variety of scientific computing applications. Several authors have reported difficulties, however, when using PINNs to…

Numerical Analysis · Mathematics 2023-10-16 Arnav Gangal , Luis Kim , Sean P. Carney

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

Optimization and Control · Mathematics 2024-09-06 Michael Hintermüller , Denis Korolev

In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on…

Neural and Evolutionary Computing · Computer Science 2024-05-21 Bo Zhang , Chao Yang

Reconstructing unknown external source functions is an important perception capability for a large range of robotics domains including manipulation, aerial, and underwater robotics. In this work, we propose a Physics-Informed Neural Network…

Robotics · Computer Science 2024-11-05 Youngsun Wi , Jayjun Lee , Miquel Oller , Nima Fazeli

This paper explores the difficulties in solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach…

Machine Learning · Computer Science 2023-06-21 Shamsulhaq Basir

In this study, Physics-Informed Neural Networks (PINNs) are skilfully applied to explore a diverse range of pulsar magneto-spheric models, specifically focusing on axisymmetric cases. The study successfully reproduced various axisymmetric…

High Energy Astrophysical Phenomena · Physics 2023-10-11 Petros Stefanou , Jorge F. Urbán , José A. Pons

The research in Artificial Intelligence methods with potential applications in science has become an essential task in the scientific community last years. Physics Informed Neural Networks (PINNs) is one of this methods and represent a…

Computational Physics · Physics 2023-07-24 Luis Medrano Navarro , Luis Martín Moreno , Sergio G Rodrigo

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

Numerical Analysis · Mathematics 2023-05-23 Victorita Dolean , Alexander Heinlein , Siddhartha Mishra , Ben Moseley

As we know differential equations are very useful for electrical engineers to solve a variety of problems like: voltage across a capacitor, input versus output voltage, etc. Therefore, the goal of this paper is to find the solutions of…

Numerical Analysis · Mathematics 2026-01-07 Vijay Kumar Patel , Abhishekh , Dileep Kumar , Nitin Kumar

Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…

Computational Physics · Physics 2024-06-10 Michel Nohra , Steven Dufour

We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…

Machine Learning · Computer Science 2023-04-05 Hubert Baty , Leo Baty