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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 networks (PINNs) have been proven as a promising way for solving various partial differential equations, especially high-dimensional ones and those with irregular boundaries. However, their capabilities in real…

Dynamical Systems · Mathematics 2026-03-27 Guojie Li , Wuyue Yang , Liu Hong

Physics-Informed Neural Networks (PINNs) have enabled significant improvements in modelling physical processes described by partial differential equations (PDEs). PINNs are based on simple architectures, and learn the behavior of complex…

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

We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal…

Machine Learning · Statistics 2024-04-03 Zhikang Dong , Pawel Polak

Physics-informed neural networks (PINNs) have shown to be an effective tool for solving forward and inverse problems of partial differential equations (PDEs). PINNs embed the PDEs into the loss of the neural network, and this PDE loss is…

Computational Physics · Physics 2023-07-19 Chenxi Wu , Min Zhu , Qinyang Tan , Yadhu Kartha , Lu Lu

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

Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…

Machine Learning · Computer Science 2025-07-21 Chenhao Si , Ming Yan

Physics-informed neural networks (PINNs) have emerged as a prominent approach for solving partial differential equations (PDEs) by minimizing a combined loss function that incorporates both boundary loss and PDE residual loss. Despite their…

Machine Learning · Computer Science 2025-01-16 Youngsik Hwang , Dong-Young Lim

Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…

Machine Learning · Computer Science 2023-07-11 Rajat Arora

Physics-Informed Neural Networks (PINNs) solve partial differential equations using deep learning. However, conventional PINNs perform pointwise predictions that neglect dependencies within a domain, which may result in suboptimal…

Machine Learning · Computer Science 2025-05-26 Mayank Nagda , Phil Ostheimer , Thomas Specht , Frank Rhein , Fabian Jirasek , Stephan Mandt , Marius Kloft , Sophie Fellenz

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

Physics-informed neural networks (PINNs) were recently proposed in [1] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution while a PDE-induced NN is coupled to the solution NN,…

Computational Physics · Physics 2019-10-22 Xiaoli Chen , Jinqiao Duan , George Em Karniadakis

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 neural networks (PINNs) are nowadays used as efficient machine learning methods for solving differential equations. However, vanilla-PINNs fail to learn complex problems as ones involving stiff ordinary differential…

Computational Physics · Physics 2023-04-18 Hubert Baty

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

Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…

Numerical Analysis · Mathematics 2026-03-04 Noura Al Helwani , Sophie Moufawad , Georges Sakr

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…

Machine Learning · Computer Science 2024-07-18 Katsiaryna Haitsiukevich , Alexander Ilin

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) have emerged as a new learning paradigm for solving partial differential equations (PDEs) by enforcing the constraints of physical equations, boundary conditions (BCs), and initial conditions (ICs)…

Machine Learning · Computer Science 2025-05-21 Chenhong Zhou , Jie Chen , Zaifeng Yang , Ching Eng Png