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This study presents a discrete physics-informed neural network (dPINN) framework, enhanced with enforced interface constraints (EIC), for modeling physical systems using the domain decomposition method (DDM). Built upon finite element-style…

Computational Engineering, Finance, and Science · Computer Science 2025-05-19 Jichao Yin , Mingxuan Li , Jianguang Fang , Hu Wang

This paper introduces a dynamic, error-bounded hierarchical matrix (H-matrix) compression method tailored for Physics-Informed Neural Networks (PINNs). The proposed approach reduces the computational complexity and memory demands of…

Machine Learning · Computer Science 2024-09-26 John Mango , Ronald Katende

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…

Machine Learning · Computer Science 2026-05-12 Mingtao Xia , Lucas Böttcher , Tom Chou

In this article, we propose a novel Stabilized Physics Informed Neural Networks method (SPINNs) for solving wave equations. In general, this method not only demonstrates theoretical convergence but also exhibits higher efficiency compared…

Numerical Analysis · Mathematics 2024-03-29 Yuling Jiao , Yuhui Liu , Jerry Zhijian Yang , Cheng Yuan

In this paper, we present the adaptive physics-informed neural networks (PINNs) for resolving three dimensional (3D) dynamic thermo-mechanical coupling problems in large-size-ratio functionally graded materials (FGMs). The physical laws…

Computational Engineering, Finance, and Science · Computer Science 2023-06-16 Lin Qiu , Yanjie Wang , Tian He , Yan Gu , Fajie Wang

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…

Computational Physics · Physics 2020-04-22 Yuyao Chen , Lu Lu , George Em Karniadakis , Luca Dal Negro

In this work, we have applied physics-informed neural networks (PINN) for solving mesh deformation problems. We used the collocation PINN method to capture the new positions of the vertex nodes while preserving the connectivity information.…

Fluid Dynamics · Physics 2023-01-18 Atakan Aygun , Romit Maulik , Ali Karakus

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

Physics-Informed Neural Networks (PINNs) recast PDE solving as an optimisation problem in function space by minimising a residual-based objective, yet many applications require additional derivative-based relations that are just as…

Machine Learning · Computer Science 2026-04-16 Kentaro Hoshisashi , Carolyn E Phelan , Paolo Barucca

Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, ensuring that such frameworks fully…

Machine Learning · Computer Science 2025-12-12 Nanxi Chen , Sifan Wang , Rujin Ma , Airong Chen , Chuanjie Cui

Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider the problem where we have data available for density gradients from Schlieren…

Numerical Analysis · Mathematics 2022-07-27 Ameya D. Jagtap , Zhiping Mao , Nikolaus Adams , George Em Karniadakis

Physics-Informed Neural Networks (PINNs) have received increased interest for forward, inverse, and surrogate modeling of problems described by partial differential equations (PDE). However, their application to multiphysics problem,…

Machine Learning · Computer Science 2022-09-09 Danial Amini , Ehsan Haghighat , Ruben Juanes

The electromagnetic inverse scattering problem (ISP), due to its inherent strong nonlinearity and severe ill-posedness, has long been a core challenge in microwave imaging. In recent years, physics-informed neural networks (PINNs) have…

Signal Processing · Electrical Eng. & Systems 2026-05-05 Shilong Sun

Physics-Informed Neural Networks (PINNs) have gained significant attention for their simplicity and flexibility in engineering and scientific computing. In this study, we introduce a normalized PINN (NPINN) framework to solve a class of…

Numerical Analysis · Mathematics 2025-03-11 Jichao Ma , Dandan Liu , Jinran Wu , Xi'an Li

Using Physics-Informed Neural Networks (PINNs) to solve a specific boundary value problem is becoming more popular as an alternative to traditional methods. However, depending on the specific problem, they could be computationally expensive…

High Energy Astrophysical Phenomena · Physics 2023-07-06 Jorge F. Urbán , Petros Stefanou , Clara Dehman , José A. Pons

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

Surrogate modeling is used to replace computationally expensive simulations. Neural networks have been widely applied as surrogate models that enable efficient evaluations over complex physical systems. Despite this, neural networks are…

Machine Learning · Computer Science 2024-02-13 Hao Chen , Gonzalo E. Constante Flores , Can Li

Physics-informed Neural Networks (PINNs) have recently emerged as a principled way to include prior physical knowledge in form of partial differential equations (PDEs) into neural networks. Although PINNs are generally viewed as mesh-free,…

Machine Learning · Computer Science 2022-10-04 Fabricio Arend Torres , Marcello Massimo Negri , Monika Nagy-Huber , Maxim Samarin , Volker Roth

Physics-informed neural networks (PINNs) have been proposed to solve two main classes of problems: data-driven solutions and data-driven discovery of partial differential equations. This task becomes prohibitive when such data is highly…

Machine Learning · Computer Science 2022-10-20 Wei Peng , Wen Yao , Weien Zhou , Xiaoya Zhang , Weijie Yao

PINN models have demonstrated capabilities in addressing fluid PDE problems, and their potential in solid mechanics is beginning to emerge. This study identifies two key challenges when using PINN to solve general solid mechanics problems.…

Computational Engineering, Finance, and Science · Computer Science 2025-06-10 Haolin Li , Yuyang Miao , Zahra Sharif Khodaei , M. H. Aliabadi