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There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Networks (PINNs). In this paper, we develop Physics Informed…

Machine Learning · Computer Science 2019-07-09 Vikas Dwivedi , Balaji Srinivasan

Physics-Informed Neural Networks (PINNs) are deep learning models that incorporate the governing physical laws of a system into the learning process, making them well-suited for solving complex scientific and engineering problems. Recently,…

Machine Learning · Computer Science 2025-07-18 Athanasios Papastathopoulos-Katsaros , Alexandra Stavrianidi , Zhandong Liu

PINNs enhance scientific computing by incorporating physical laws into neural network structures, leading to significant advancements in scientific computing. However, PINNs struggle with multi-scale and high-frequency problems due to…

Machine Learning · Computer Science 2026-02-09 Guokan Chen , Yao Xiao , Bin Fan , Meixin Xionga , Zhicheng Lin , Yuanying Liu

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…

Machine Learning · Computer Science 2026-02-03 Olaf Yunus Laitinen Imanov

Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several…

Computational Engineering, Finance, and Science · Computer Science 2022-11-29 Diab W. Abueidda , Seid Koric , Erman Guleryuz , Nahil A. Sobh

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) are becoming a popular method for solving PDEs, due to their mesh-free nature and their ability to handle high-dimensional problems where traditional numerical solvers often struggle. Despite their…

Numerical Analysis · Mathematics 2025-08-26 Yuzhen Li , Liang Li , Stéphane Lanteri , Bin Li

Deep learning techniques with neural networks have been used effectively in computational fluid dynamics (CFD) to obtain solutions to nonlinear differential equations. This paper presents a physics-informed neural network (PINN) approach to…

Machine Learning · Computer Science 2023-07-25 Greeshma Krishna , Malavika S Nair , Pramod P Nair , Anil Lal S

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

This work aims to provide an effective deep learning framework to predict the vector-soliton solutions of the coupled nonlinear equations and their interactions. The method we propose here is a physics-informed neural network (PINN)…

Numerical Analysis · Mathematics 2022-11-23 Shu-Mei Qin , Min Li , Tao Xu , Shao-Qun Dong

Deep neural networks (DNNs), especially physics-informed neural networks (PINNs), have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). However, these methods…

Machine Learning · Computer Science 2023-10-26 Wenbo Cao , Weiwei Zhang

This work proposes a wavelet-based physics-informed quantum neural network framework to efficiently address multiscale partial differential equations that involve sharp gradients, stiffness, rapid local variations, and highly oscillatory…

Machine Learning · Computer Science 2025-12-10 Deepak Gupta , Himanshu Pandey , Ratikanta Behera

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) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accurately while alleviating the need for supervised learning to a…

Computational Physics · Physics 2020-08-26 Xuhui Meng , Zhen Li , Dongkun Zhang , George Em Karniadakis

In this study, we utilize the emerging Physics Informed Neural Networks (PINNs) approach for the first time to predict the flow field of a compressor cascade. Different from conventional training methods, a new adaptive learning strategy…

Machine Learning · Computer Science 2024-05-08 Zhihui Li , Francesco Montomoli , Sanjiv Sharma

Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in…

Machine Learning · Computer Science 2022-09-19 Shihong Zhang , Chi Zhang , Bosen Wang

Physics-informed neural networks (PINNs) are trained using physical equations and can also incorporate unmodeled effects by learning from data. PINNs for control (PINCs) of dynamical systems are gaining interest due to their prediction…

Systems and Control · Electrical Eng. & Systems 2024-08-29 Henrik Krauss , Tim-Lukas Habich , Max Bartholdt , Thomas Seel , Moritz Schappler

Solving coupled systems of differential equations (DEs) is a central problem across scientific computing. While Physics Informed Neural Networks (PINNs) offer a promising, mesh-free approach, their standard architectures struggle with the…

Quantum Physics · Physics 2026-02-17 Zhao-Wei Wang , Zhao-Ming Wang

We demonstrate the utility of physics-informed neural networks (PINNs) as solvers for the non-relativistic, time-dependent Schr\"odinger equation. We study the performance and generalisability of PINN solvers on the time evolution of a…

Quantum Physics · Physics 2022-10-25 Karan Shah , Patrick Stiller , Nico Hoffmann , Attila Cangi

There has been a growing interest in the use of Deep Neural Networks (DNNs) to solve Partial Differential Equations (PDEs). Despite the promise that such approaches hold, there are various aspects where they could be improved. Two such…

Machine Learning · Computer Science 2022-12-26 Amuthan A. Ramabathiran , Prabhu Ramachandran
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