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Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE residual as the loss function. This strategy is called "physics-informed neural networks" (PINNs), but it currently cannot produce high-accuracy…

Machine Learning · Computer Science 2024-04-11 Qi Zeng , Yash Kothari , Spencer H. Bryngelson , Florian Schäfer

Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations (PDEs). We employ PINNs for solving the Reynolds-averaged Navier$\unicode{x2013}$Stokes…

Fluid Dynamics · Physics 2022-07-20 Hamidreza Eivazi , Mojtaba Tahani , Philipp Schlatter , Ricardo Vinuesa

Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) from a variety of experimental perspectives. Some recent studies have also proposed PINN algorithms for PDEs on…

Numerical Analysis · Mathematics 2024-08-06 Guanhang Lei , Zhen Lei , Lei Shi , Chenyu Zeng , Ding-Xuan Zhou

As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…

Machine Learning · Computer Science 2021-11-11 Yuhao Huang

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

Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the…

Machine Learning · Computer Science 2024-01-17 Abdul Hannan Mustajab , Hao Lyu , Zarghaam Rizvi , Frank Wuttke

The recently developed physics-informed machine learning has made great progress for solving nonlinear partial differential equations (PDEs), however, it may fail to provide reasonable approximations to the PDEs with discontinuous…

Numerical Analysis · Mathematics 2021-12-06 Chunyue Lv , Lei Wang , Chenming Xie

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…

Machine Learning · Computer Science 2024-08-20 Woojin Cho , Minju Jo , Haksoo Lim , Kookjin Lee , Dongeun Lee , Sanghyun Hong , Noseong Park

Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of…

Machine Learning · Computer Science 2024-05-15 Lena Podina , Mahdi Torabi Rad , Mohammad Kohandel

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

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

Numerical Analysis · Mathematics 2023-05-23 Victorita Dolean , Alexander Heinlein , Siddhartha Mishra , Ben Moseley

In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solution for partial differential equations (PDEs) in case of arbitrary geometries while strictly enforcing…

Numerical Analysis · Mathematics 2024-07-30 Hamed Saidaoui , Luis Espath , Rául Tempone

Physics-informed neural networks (PINNs) offer a promising avenue for tackling both forward and inverse problems in partial differential equations (PDEs) by incorporating deep learning with fundamental physics principles. Despite their…

Machine Learning · Computer Science 2024-02-06 Hemanth Saratchandran , Shin-Fang Chng , Simon Lucey

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 approximation of solutions of partial differential equations (PDEs) with numerical algorithms is a central topic in applied mathematics. For many decades, various types of methods for this purpose have been developed and extensively…

Numerical Analysis · Mathematics 2024-08-26 Lukas Gonon , Arnulf Jentzen , Benno Kuckuck , Siyu Liang , Adrian Riekert , Philippe von Wurstemberger

Physics-informed neural networks (PINNs) are numerical solvers that embed all the physical information of a system into the loss function of a neural network. In this way the learned solution accounts for data (if available), the governing…

Computational Physics · Physics 2025-07-30 Andrés Martínez-Esteban , Pablo Calvo-Barlés , Luis Martín-Moreno , Sergio G Rodrigo

Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. In forward modeling problems, PINNs are meshless partial…

Machine Learning · Computer Science 2023-11-28 Yicheng Wang , Xiaotian Han , Chia-Yuan Chang , Daochen Zha , Ulisses Braga-Neto , Xia Hu

Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem,…

Numerical Analysis · Mathematics 2024-10-21 Sidi Wu

Physics-informed neural networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…

Computational Physics · Physics 2026-03-25 Guoqiang Lei , D. Exposito , Xuerui Mao

The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and validated to find solutions to both linear and non-linear partial…

Machine Learning · Computer Science 2024-03-28 Vikas Dwivedi , Nishant Parashar , Balaji Srinivasan