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Physics-Informed Neural Networks (PINNs) have gained much attention in various fields of engineering thanks to their capability of incorporating physical laws into the models. PINNs integrate the physical constraints by minimizing the…

Machine Learning · Computer Science 2025-07-28 Thi Nguyen Khoa Nguyen , Thibault Dairay , Raphaël Meunier , Christophe Millet , Mathilde Mougeot

Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to…

Numerical Analysis · Mathematics 2024-11-28 Marco Berardi , Fabio Difonzo , Matteo Icardi

Compartmental models provide simple and efficient tools to analyze the relevant transmission processes during an outbreak, to produce short-term forecasts or transmission scenarios, and to assess the impact of vaccination campaigns.…

Numerical Analysis · Mathematics 2025-02-19 Caterina Millevoi , Damiano Pasetto , Massimiliano Ferronato

Physics-informed neural network (PINN) is a powerful emerging method for studying forward-inverse problems of partial differential equations (PDEs), even from limited sample data. Variable coefficient PDEs, which model real-world phenomena,…

Computational Physics · Physics 2025-03-07 Hui-Juan Zhou , Yong Chen

Physics Informed Neural Networks (PINNs) have frequently been used for the numerical approximation of Partial Differential Equations (PDEs). The goal of this paper is to construct PINNs along with a computable upper bound of the error,…

Numerical Analysis · Mathematics 2022-12-19 Lewin Ernst , Karsten Urban

This paper develops a novel deep learning approach for solving evolutionary equations, which integrates sequential learning strategies with an enhanced hard constraint strategy featuring trainable parameters, addressing the low…

Machine Learning · Computer Science 2025-03-25 Yushi Zhang , Shuai Su , Yong Wang , Yanzhong Yao

Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that…

Machine Learning · Statistics 2025-11-20 Georgios Venianakis , Constantinos Theodoropoulos , Michail Kavousanakis

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

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

Nonlinear partial differential equations (PDEs) are pivotal in modeling complex physical systems, yet traditional Physics-Informed Neural Networks (PINNs) often struggle with unresolved residuals in critical spatiotemporal regions and…

Machine Learning · Computer Science 2026-04-03 Ziyang Zhang , Feifan Zhang , Weidong Tang , Lei Shi , Tailai Chen

In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…

Numerical Analysis · Mathematics 2024-09-05 Xiaodong Feng , Haojiong Shangguan , Tao Tang , Xiaoliang Wan , Tao Zhou

Physics-informed neural networks (PINNs) are an emerging technique to solve partial differential equations (PDEs). In this work, we propose a simple but effective PINN approach for the phase-field model of ferroelectric microstructure…

Materials Science · Physics 2024-09-06 Lan Shang , Sizheng Zheng , Jin Wang , Jie Wang

Physics-informed neural networks (PINNs) are known to suffer from optimization difficulty. In this work, we reveal the connection between the optimization difficulty of PINNs and activation functions. Specifically, we show that PINNs…

Machine Learning · Computer Science 2023-11-27 Honghui Wang , Lu Lu , Shiji Song , Gao Huang

Physics-informed neural networks (PINNs) incorporate physical laws into their training to efficiently solve partial differential equations (PDEs) with minimal data. However, PINNs fail to guarantee adherence to conservation laws, which are…

Machine Learning · Computer Science 2024-10-24 Anthony Baez , Wang Zhang , Ziwen Ma , Subhro Das , Lam M. Nguyen , Luca Daniel

Physics-informed Neural Network (PINN) is a promising tool that has been applied in a variety of physical phenomena described by partial differential equations (PDE). However, it has been observed that PINNs are difficult to train in…

Fluid Dynamics · Physics 2023-07-19 E. J. R. Coutinho , M. Dall'Aqua , L. McClenny , M. Zhong , U. Braga-Neto , E. Gildin

Stiff differential equations are prevalent in various scientific domains, posing significant challenges due to the disparate time scales of their components. As computational power grows, physics-informed neural networks (PINNs) have led to…

Machine Learning · Computer Science 2025-01-30 Emilien Seiler , Wanzhou Lei , Pavlos Protopapas

In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…

Systems and Control · Electrical Eng. & Systems 2024-03-12 Huynh T. T. Tran , Hieu T. Nguyen

"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) 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

Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft…

Machine Learning · Computer Science 2022-12-09 Rambod Mojgani , Maciej Balajewicz , Pedram Hassanzadeh