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Related papers: Finite-PINN: A Physics-Informed Neural Network wit…

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Singularly perturbed problems are known to have solutions with steep boundary layers that are hard to resolve numerically. Traditional numerical methods, such as Finite Difference Methods (FDMs), require a refined mesh to obtain stable and…

Numerical Analysis · Mathematics 2024-09-13 Jiajing Guan , Howard Elman

This study introduces a computational approach leveraging Physics-Informed Neural Networks (PINNs) for the efficient computation of arterial blood flows, particularly focusing on solving the incompressible Navier-Stokes equations by using…

Numerical Analysis · Mathematics 2024-04-29 Shivam Bhargava , Nagaiah Chamakuri

Physics-informed neural networks (PINNs) are a simple surrogate-modelling paradigm for partial differential equations, but their standard strong-form residual formulation is ill suited to the shallow water equations (SWE). It cannot enforce…

Machine Learning · Computer Science 2026-05-13 Xiaofeng Liu

While Physics-Informed Neural Networks (PINNs) offer a mesh-free approach to solving PDEs, standard point-wise residual minimization suffers from convergence pathologies in topologically complex domains like Triply Periodic Minimal Surfaces…

Machine Learning · Computer Science 2026-03-11 Weizheng Zhang , Xunjie Xie , Hao Pan , Xiaowei Duan , Bingteng Sun , Qiang Du , Lin Lu

Physics-Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by embedding governing equations and boundary/initial conditions into the loss function. However, enforcing Dirichlet boundary conditions accurately…

Machine Learning · Computer Science 2025-01-15 Nahil Sobh , Rini Jasmine Gladstone , Hadi Meidani

Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining…

Machine Learning · Computer Science 2024-10-07 Feilong Jiang , Xiaonan Hou , Min Xia

Physics-informed neural networks (PINNs) are able to solve partial differential equations (PDEs) by incorporating the residuals of the PDEs into their loss functions. Variational Physics-Informed Neural Networks (VPINNs) and hp-VPINNs use…

Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on…

Machine Learning · Computer Science 2025-12-11 Jinming Lu , Jiayi Tian , Yequan Zhao , Hai Li , Zheng Zhang

Form-finding of unilateral membrane structures is commonly addressed by solving equilibrium equations with Finite Element Methods (FEMs). This paper investigates Physics-Informed Neural Networks (PINNs) as an alternative, where the…

Computational Engineering, Finance, and Science · Computer Science 2026-05-05 Luigi Sibille , Sigrid Adriaenssens , Carlo Olivieri

Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…

Machine Learning · Computer Science 2022-11-02 Raphaël Pellegrin , Blake Bullwinkel , Marios Mattheakis , Pavlos Protopapas

The vibrational response of structural components carries valuable information about their underlying mechanical properties, health status and operational conditions. This underscores the need for the development of efficient physics-based…

Applied Physics · Physics 2024-09-18 Saeid Hedayatrasa , Olga Fink , Wim Van Paepegem , Mathias Kersemans

Modeling self-gravitating gas flows is essential to answering many fundamental questions in astrophysics. This spans many topics including planet-forming disks, star-forming clouds, galaxy formation, and the development of large-scale…

Machine Learning · Computer Science 2023-08-17 Sayantan Auddy , Ramit Dey , Neal J. Turner , Shantanu Basu

The recent surge of interest in physics-informed neural network (PINN) methods has led to a wave of studies that attest to their potential for solving partial differential equations (PDEs) and predicting the dynamics of physical systems.…

Computational Engineering, Finance, and Science · Computer Science 2023-06-02 Pi-Yueh Chuang , Lorena A. Barba

Most noninvasive imaging techniques utilize electromagnetic or acoustic waves originating from multiple locations and directions to identify hidden geometrical structures. Surprisingly, it is also possible to image hidden voids and…

Computational Engineering, Finance, and Science · Computer Science 2025-02-18 Saviz Mowlavi , Ken Kamrin

Physics-Informed Neural Networks (PINNs) have shown promise in solving incompressible Navier-Stokes equations, yet existing approaches are predominantly designed for single-flow settings. When extended to multi-flow scenarios, these methods…

Computer Vision and Pattern Recognition · Computer Science 2026-03-12 Dengdi Sun , Jie Chen , Xiao Wang , Jin Tang

Physics-Informed Neural Networks (PINNs) have emerged as a highly active research topic across multiple disciplines in science and engineering, including computational geomechanics. PINNs offer a promising approach in different applications…

Computational Engineering, Finance, and Science · Computer Science 2024-04-30 Yared W. Bekele

In this work, a model based on the Physics - Informed Neural Networks (PINNs) for solving elastic deformation of heterogeneous solids and associated Uncertainty Quantification (UQ) is presented. For the present study, the PINNs framework -…

This dissertation investigates physics-informed neural networks (PINNs) as candidate models for encoding governing equations, and assesses their performance on experimental data from two different systems. The first system is a simple…

Machine Learning · Computer Science 2024-01-09 Hamza Alsharif

Physics-informed neural network (PINN) is a data-driven approach to solve equations. It is successful in many applications; however, the accuracy of the PINN is not satisfactory when it is used to solve multiscale equations. Homogenization…

Numerical Analysis · Mathematics 2021-08-31 Wing Tat Leung , Guang Lin , Zecheng Zhang

Motivated by recent research on Physics-Informed Neural Networks (PINNs), we make the first attempt to introduce the PINNs for numerical simulation of the elliptic Partial Differential Equations (PDEs) on 3D manifolds. PINNs are one of the…

Numerical Analysis · Mathematics 2021-03-05 Zhuochao Tang , Zhuojia Fu