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In this study, the capabilities of the Physics-Informed Neural Network (PINN) method are investigated for three major tasks: modeling, simulation, and optimization in the context of the heat conduction problem. In the modeling phase, the…

Computational Physics · Physics 2025-10-31 Ehsan Ghaderi , Mohamad Ali Bijarchi , Siamak Kazemzadeh Hannani , Ali Nouri Boroujerdi

The placement of temperature sensitive and safety-critical components is crucial in the automotive industry. It is therefore inevitable, even at the design stage of new vehicles that these components are assessed for potential safety…

Machine Learning · Computer Science 2022-03-23 Philip Heger , Markus Full , Daniel Hilger , Norbert Hosters

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

Due to divergence instability, the accuracy of low-order conforming finite element methods for nearly incompressible elasticity equations deteriorates as the Lam\'e coefficient $\lambda\to\infty$, or equivalently as the Poisson ratio…

Numerical Analysis · Mathematics 2025-10-24 Josef Dick , Seungchan Ko , Quoc Thong Le Gia , Kassem Mustapha , Sanghyeon Park

A physics-informed neural network (PINN) that combines deep learning with physics is studied to solve the nonlinear Schr\"odinger equation for learning nonlinear dynamics in fiber optics. We carry out a systematic investigation and…

Optics · Physics 2021-09-03 Xiaotian Jiang , Danshi Wang , Qirui Fan , Min Zhang , Chao Lu , Alan Pak Tao Lau

Physics-Informed Neural Networks (PINNs) are a class of deep neural networks that are trained, using automatic differentiation, to compute the response of systems governed by partial differential equations (PDEs). The training of PINNs is…

Machine Learning · Computer Science 2021-04-27 Mohammad Amin Nabian , Rini Jasmine Gladstone , Hadi Meidani

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving Partial Differential Equations (PDEs) by incorporating physical constraints into deep learning models. However, standard PINNs often require a large…

Machine Learning · Computer Science 2025-05-05 Keon Vin Park

Physics-informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering…

Computational Engineering, Finance, and Science · Computer Science 2022-10-05 Shahed Rezaei , Ali Harandi , Ahmad Moeineddin , Bai-Xiang Xu , Stefanie Reese

Physics-Informed machine learning models have recently emerged with some interesting and unique features that can be applied to reservoir engineering. In particular, physics-informed neural networks (PINN) leverage the fact that neural…

Fluid Dynamics · Physics 2023-12-01 Daniel Badawi , Eduardo Gildin

Accurate vessel trajectory prediction is crucial for navigational safety, route optimization, traffic management, search and rescue operations, and autonomous navigation. Traditional data-driven models lack real-world physical constraints,…

Machine Learning · Computer Science 2025-06-17 Md Mahbub Alam , Amilcar Soares , José F. Rodrigues-Jr , Gabriel Spadon

The physics-informed neural network (PINN) is effective in solving the partial differential equation (PDE) by capturing the physics constraints as a part of the training loss function through the Automatic Differentiation (AD). This study…

Computational Physics · Physics 2022-02-17 Zixue Xiang , Wei Peng , Weien Zhou , Wen Yao

Accurate computational modeling of damage and fracture remains a central challenge in solid mechanics. The finite element method (FEM) is widely used for numerical modeling of fracture problems; however, classical damage models without…

Soft Condensed Matter · Physics 2025-11-07 Aditya Konale , Vikas Srivastava

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

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 Networks (PINNs) have been recognized as a mesh-free alternative to solve partial differential equations where physics information is incorporated. However, in dealing with problems characterized by high stiffness or…

Machine Learning · Computer Science 2026-03-04 Divyavardhan Singh , Shubham Kamble , Dimple Sonone , Kishor Upla

I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the…

Computational Physics · Physics 2024-03-04 Hubert Baty

In this paper, we develop a physics-informed neural network (PINN) model for parabolic problems with a sharply perturbed initial condition. As an example of a parabolic problem, we consider the advection-dispersion equation (ADE) with a…

Numerical Analysis · Mathematics 2023-06-28 Yifei Zong , QiZhi He , Alexandre M. Tartakovsky

Physics-informed neural networks (PINNs) have shown remarkable prospects in solving partial differential equations (PDEs) involving fluid mechanics. However, the method has so far succeeded only in inviscid flows and incompressible viscous…

Fluid Dynamics · Physics 2026-02-24 Jiahao Song , Wenbo Cao , Weiwei Zhang

Physics-informed neural networks (PINNs) have received significant attention as a unified framework for forward, inverse, and surrogate modeling of problems governed by partial differential equations (PDEs). Training PINNs for forward…

Machine Learning · Computer Science 2022-06-22 Ehsan Haghighat , Danial Amini , Ruben Juanes

Systems biology and systems neurophysiology in particular have recently emerged as powerful tools for a number of key applications in the biomedical sciences. Nevertheless, such models are often based on complex combinations of multiscale…

Neural and Evolutionary Computing · Computer Science 2022-09-27 Matteo Ferrante , Andera Duggento , Nicola Toschi