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Related papers: PinnDE: Physics-Informed Neural Networks for Solvi…

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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

In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design…

Machine Learning · Computer Science 2023-10-17 Woojin Cho , Kookjin Lee , Donsub Rim , Noseong Park

We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale,…

Computational Physics · Physics 2020-06-23 Ben Moseley , Andrew Markham , Tarje Nissen-Meyer

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

In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate…

Numerical Analysis · Mathematics 2025-08-12 Feng Han , Jianguo Wang , Guoliang Peng , Xueting Shi

In this paper, we review the new method Physics-Informed Neural Networks (PINNs) that has become the main pillar in scientific machine learning, we present recent practical extensions, and provide a specific example in data-driven discovery…

Machine Learning · Computer Science 2024-09-02 Maziar Raissi , Paris Perdikaris , Nazanin Ahmadi , George Em Karniadakis

A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…

Numerical Analysis · Mathematics 2022-03-17 Revanth Mattey , Susanta Ghosh

This paper explores the difficulties in solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach…

Machine Learning · Computer Science 2023-06-21 Shamsulhaq Basir

Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we…

Machine Learning · Computer Science 2025-09-25 Javier Castro , Benjamin Gess

Physics-Informed Neural Networks (PINNs) recast PDE solving as an optimisation problem in function space by minimising a residual-based objective, yet many applications require additional derivative-based relations that are just as…

Machine Learning · Computer Science 2026-04-16 Kentaro Hoshisashi , Carolyn E Phelan , Paolo Barucca

Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…

Machine Learning · Computer Science 2025-07-21 Chenhao Si , Ming Yan

In recent engineering applications using deep learning, physics-informed neural network (PINN) is a new development as it can exploit the underlying physics of engineering systems. The novelty of PINN lies in the use of partial differential…

Computational Engineering, Finance, and Science · Computer Science 2026-02-26 Kart Leong Lim , Rahul Dutta , Mihai Rotaru

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 networks (PINNs) have emerged as promising surrogate modes for solving partial differential equations (PDEs). Their effectiveness lies in the ability to capture solution-related features through neural networks.…

Machine Learning · Computer Science 2023-07-13 Junjun Yan , Xinhai Chen , Zhichao Wang , Enqiang Zhou , Jie Liu

Physics Informed Neural Networks (PINNs) have been emerging as a powerful computational tool for solving differential equations. However, the applicability of these models is still in its initial stages and requires more standardization to…

Computational Engineering, Finance, and Science · Computer Science 2025-05-30 Afila Ajithkumar Sophiya , Akarsh K Nair , Sepehr Maleki , Senthil K. Krishnababu

This paper puts forward the vision of creating a library of neural-network-based models for power system simulations. Traditional numerical solvers struggle with the growing complexity of modern power systems, necessitating faster and more…

Systems and Control · Electrical Eng. & Systems 2025-02-11 Ioannis Karampinis , Petros Ellinas , Ignasi Ventura Nadal , Rahul Nellikkath , Spyros Chatzivasileiadis

Scientific machine learning (SciML) represents a significant advancement in integrating machine learning (ML) with scientific methodologies. At the forefront of this development are Physics-Informed Neural Networks (PINNs), which offer a…

Machine Learning · Computer Science 2024-11-19 Reyhaneh Taj

PDEs arise ubiquitously in science and engineering, where solutions depend on parameters (physical properties, boundary conditions, geometry). Traditional numerical methods require re-solving the PDE for each parameter, making parameter…

Machine Learning · Statistics 2026-02-02 Zhuo Zhang , Xiong Xiong , Sen Zhang , Yuan Zhao , Xi Yang

We explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the…

Machine Learning · Computer Science 2025-03-11 Zongren Zou , Zhicheng Wang , George Em Karniadakis

Physics-informed neural networks (PINNs) hold the potential for supplementing the existing set of techniques for solving differential equations that emerge in the study of black hole quasinormal modes. The present research investigated them…

General Relativity and Quantum Cosmology · Physics 2021-08-13 Anele M Ncube , Gerhard E Harmsen , Alan S Cornell