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Physics-informed neural networks (PINNs) have recently emerged as a novel and popular approach for solving forward and inverse problems involving partial differential equations (PDEs). However, achieving stable training and obtaining…

Fluid Dynamics · Physics 2024-05-28 Wenbo Cao , Weiwei Zhang

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…

Numerical Analysis · Mathematics 2024-11-20 Tim De Ryck , Siddhartha Mishra

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

Machine Learning · Computer Science 2025-03-25 Edgar Torres , Jonathan Schiefer , Mathias Niepert

In recent years, Physics-Informed Neural Networks (PINNs) have become a representative method for solving partial differential equations (PDEs) with neural networks. PINNs provide a novel approach to solving PDEs through optimization…

Computational Physics · Physics 2024-11-28 Weiwei Zhang , Wei Suo , Jiahao Song , Wenbo Cao

"AI for Science" aims to solve fundamental scientific problems using AI techniques. As most physical phenomena can be described as Partial Differential Equations (PDEs) , approximating their solutions using neural networks has evolved as a…

Machine Learning · Computer Science 2024-07-31 Mohan Ren , Zhihao Fang , Keren Li , Anirbit Mukherjee

Physics-informed neural networks (PINNs) are a versatile tool in the burgeoning field of scientific machine learning for solving partial differential equations (PDEs). However, determining suitable training strategies for them is not…

Numerical Analysis · Mathematics 2026-03-09 Saad Qadeer , Panos Stinis

In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…

Machine Learning · Computer Science 2025-11-19 Tyrus Whitman , Andrew Particka , Christopher Diers , Ian Griffin , Charuka Wickramasinghe , Pradeep Ranaweera

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

Numerical Analysis · Mathematics 2022-08-29 Antonio Tadeu Azevedo Gomes , Larissa Miguez da Silva , Frederic Valentin

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

Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws…

Machine Learning · Computer Science 2025-06-09 Wenxuan Huo , Qiang He , Gang Zhu , Weifeng Huang

Physics-informed neural networks (PINNs) have recently emerged as a popular approach for solving forward and inverse problems involving partial differential equations (PDEs). Compared to fully connected neural networks, PINNs based on…

Numerical Analysis · Mathematics 2025-08-06 Jiahao Song , Wenbo Cao , Weiwei Zhang

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) have recently emerged as a promising way to compute the solutions of partial differential equations (PDEs) using deep neural networks. However, despite their significant success in various fields, it…

Numerical Analysis · Mathematics 2024-07-15 Seungchan Ko , Sang Hyeon Park

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

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…

Machine Learning · Computer Science 2023-04-12 Aleksandr Dekhovich , Marcel H. F. Sluiter , David M. J. Tax , Miguel A. Bessa

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 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) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs are known to be robust for smaller training sets, derive better generalization…

Machine Learning · Computer Science 2024-06-19 Birgit Hillebrecht , Benjamin Unger

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

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
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