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Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space--time PINNs take…

Machine Learning · Computer Science 2026-01-29 Chen-Yang Dai , Che-Chia Chang , Te-Sheng Lin , Ming-Chih Lai , Chieh-Hsin Lai

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

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

Physics-informed neural networks (PINNs) have recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by…

Machine Learning · Computer Science 2025-12-22 Zhaoqian Gao , Min Yanga

Physics-Informed Neural Networks (PINN) are neural networks encoding the problem governing equations, such as Partial Differential Equations (PDE), as a part of the neural network. PINNs have emerged as a new essential tool to solve various…

Numerical Analysis · Mathematics 2021-07-07 Stefano Markidis

Physics-Informed Neural Networks (PINNs) combine deep learning with physical constraints for solving partial differential equations (PDEs), and are widely applied in fluid mechanics, heat transfer, and solid mechanics. However, PINN…

Machine Learning · Computer Science 2026-05-18 Xujia Chen , Xinyue Hu , Letian Chen , Daming Shi , Wenhui Fan

Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast…

Machine Learning · Computer Science 2023-06-19 Junjun Yan , Xinhai Chen , Zhichao Wang , Enqiang Zhoui , Jie Liu

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

The solution of partial differential equations (PDES) on irregular domains has long been a subject of significant research interest. In this work, we present an approach utilizing physics-informed neural networks (PINNs) to achieve…

Computational Physics · Physics 2025-06-12 Cuizhi Zhou , Kaien Zhu

We present a novel numerical approach aiming at computing equilibria and dynamics structures of magnetized plasmas in coronal environments. A technique based on the use of neural networks that integrates the partial differential equations…

Solar and Stellar Astrophysics · Physics 2023-10-30 Hubert Baty , Vincent Vigon

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) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in…

Machine Learning · Computer Science 2023-12-19 Rini J. Gladstone , Mohammad A. Nabian , N. Sukumar , Ankit Srivastava , Hadi Meidani

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for integrating physics-based constraints and data to address forward and inverse problems in machine learning. Despite their potential, the implementation of PINNs…

Optimization and Control · Mathematics 2024-12-19 Alan Williams , Christopher Leon , Alexander Scheinker

We present a new technique for the accelerated training of physics-informed neural networks (PINNs): discretely-trained PINNs (DT-PINNs). The repeated computation of partial derivative terms in the PINN loss functions via automatic…

Machine Learning · Computer Science 2023-01-31 Ramansh Sharma , Varun Shankar

Physics-informed neural networks (PINNs) have been popularized as a deep learning framework that can seamlessly synthesize observational data and partial differential equation (PDE) constraints. Their practical effectiveness however can be…

Machine Learning · Computer Science 2023-08-17 Sifan Wang , Shyam Sankaran , Hanwen Wang , Paris Perdikaris

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training. However, traditional PINN models are typically designed…

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

Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…

Machine Learning · Computer Science 2024-10-22 Hamid El Bahja , Jan Christian Hauffen , Peter Jung , Bubacarr Bah , Issa Karambal

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

Physics-informed neural networks (PINNs) have recently emerged as promising data-driven PDE solvers showing encouraging results on various PDEs. However, there is a fundamental limitation of training PINNs to solve multi-dimensional PDEs…

Machine Learning · Computer Science 2023-11-01 Junwoo Cho , Seungtae Nam , Hyunmo Yang , Seok-Bae Yun , Youngjoon Hong , Eunbyung Park

With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs. Physics-informed neural networks (PINNs) have recently emerged and succeeded…

Machine Learning · Computer Science 2023-02-07 Namgyu Kang , Byeonghyeon Lee , Youngjoon Hong , Seok-Bae Yun , Eunbyung Park