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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

This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results…

Numerical Analysis · Mathematics 2023-02-09 Pongpisit Thanasutives , Takashi Morita , Masayuki Numao , Ken-ichi Fukui

In this paper, we investigate the forward problems on the data-driven rational solitons for the (2+1)-dimensional KP-I equation and spin-nonlinear Schr\"odinger (spin-NLS) equation via the deep neural networks leaning. Moreover, the inverse…

Pattern Formation and Solitons · Physics 2021-12-30 Zijian Zhou , Li Wang , Zhenya Yan

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) is becoming a popular alternative method for solving partial differential equations (PDEs). However, they require dedicated manual modifications to the hyperparameters of the network, the sampling…

Computational Engineering, Finance, and Science · Computer Science 2025-04-15 Rui Zhang , Liang Li , Stéphane Lanteri , Hao Kang , Jiaqi Li

Quantum state tomography (QST) faces exponential measurement requirements and noise sensitivity in multi-qubit systems, bottlenecking practical quantum technologies. We present a physics-informed neural network (PINN) framework integrating…

Quantum Physics · Physics 2025-12-17 Changchun Feng , Laifa Tao , Lin Chen

An improved physics-informed neural network (IPINN) algorithm with four output functions and four physics constraints, which possesses neuron-wise locally adaptive activation function and slope recovery term, is appropriately proposed to…

Pattern Formation and Solitons · Physics 2022-06-01 Juncai Pu , Yong Chen

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

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

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 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

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) show great advantages in solving partial differential equations. In this paper, we for the first time propose to study conformable time fractional diffusion equations by using PINNs. By solving the…

Numerical Analysis · Mathematics 2021-08-18 Yinlin Ye , Yajing Li , Hongtao Fan , Xinyi Liu , Hongbing Zhang

Interest is rising in Physics-Informed Neural Networks (PINNs) as a mesh-free alternative to traditional numerical solvers for partial differential equations (PDEs). However, PINNs often struggle to learn high-frequency and multi-scale…

Machine Learning · Computer Science 2025-02-25 Madison Cooley , Varun Shankar , Robert M. Kirby , Shandian Zhe

The physics informed neural network (PINN) is a promising method for solving time-evolution partial differential equations (PDEs). However, the standard PINN method may fail to solve the PDEs with strongly nonlinear characteristics or those…

Numerical Analysis · Mathematics 2023-06-08 Jiawei Guo , Yanzhong Yao , Han Wang , Tongxiang Gu

This paper focuses on the PINNs algorithm by proposing the ALM-PINNs computational framework to solve various nonlinear partial differential equations and corresponding parameters identification problems. The numerical solutions obtained by…

Numerical Analysis · Mathematics 2024-10-15 Yimeng Tian , Dinghua Xu

We introduce Structure Informed Neural Networks (SINNs), a novel method for solving boundary observation problems involving PDEs. The SINN methodology is a data-driven framework for creating approximate solutions to internal variables on…

Fluid Dynamics · Physics 2023-10-31 Jakub Horsky , Andrew Wynn

Nonlinear Partial Differential Equations (PDEs) are ubiquitous in mathematical physics and engineering. Although Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving PDE problems, they typically struggle to…

Numerical Analysis · Mathematics 2026-04-02 Sean Disarò , Ruma Rani Maity , Aras Bacho

Physics-Informed Neural Networks (PINNs) offer a flexible paradigm for solving differential equations by embedding governing laws into the training objective. A persistent limitation is instance specificity: standard PINNs typically require…

Machine Learning · Computer Science 2026-05-05 Yiqi Rao , Pavlos Protopapas

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional…