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Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

Numerical Analysis · Mathematics 2023-05-23 Victorita Dolean , Alexander Heinlein , Siddhartha Mishra , Ben Moseley

Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…

Computational Engineering, Finance, and Science · Computer Science 2022-01-26 Han Gao , Matthew J. Zahr , Jian-Xun Wang

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

Despite their ubiquity, the rich physics present in a plasma sheath has inhibited the development of a generally applicable description of this critical region. The present study utilizes a physics-informed neural network (PINN) to evaluate…

Plasma Physics · Physics 2026-04-27 Ethan Webb , Yuzhi Li , Christopher McDevitt

Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…

Machine Learning · Computer Science 2023-05-08 Chandrajit Bajaj , Luke McLennan , Timothy Andeen , Avik Roy

Physics-Informed Neural Networks (PINNs) solve physical systems by incorporating governing partial differential equations directly into neural network training. In electromagnetism, where well-established methodologies such as FDTD and FEM…

Computational Physics · Physics 2026-02-13 Nilufer K. Bulut

Physics-Informed Neural Networks (PINNs) have received increased interest for forward, inverse, and surrogate modeling of problems described by partial differential equations (PDE). However, their application to multiphysics problem,…

Machine Learning · Computer Science 2022-09-09 Danial Amini , Ehsan Haghighat , Ruben Juanes

Physics-Informed Neural Networks (PINNs) show significant potential for solving inverse problems, especially when observations are limited and sparse, provided that the relevant physical equations are known. We use PINNs to estimate smooth…

Numerical Analysis · Mathematics 2025-08-06 Moises Sierpe , Ernesto Castillo , Hernan Mella , Felipe Galarce

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

Physics-Informed Neural Networks (PINNs) are a novel computational approach for solving partial differential equations (PDEs) with noisy and sparse initial and boundary data. Although, efficient quantification of epistemic and aleatoric…

Machine Learning · Computer Science 2025-05-02 Júlia Vicens Figueres , Juliette Vanderhaeghen , Federica Bragone , Kateryna Morozovska , Khemraj Shukla

Physics-informed neural networks (PINNs) have recently received much attention due to their capabilities in solving both forward and inverse problems. For training a deep neural network associated with a PINN, one typically constructs a…

Machine Learning · Computer Science 2022-08-26 Pouyan Nasiri , Roozbeh Dargazany

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

Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…

Soft- and hard-constrained Physics Informed Neural Networks (PINNs) have achieved great success in solving partial differential equations (PDEs). However, these methods still face great challenges when solving the Navier-Stokes equations…

Fluid Dynamics · Physics 2024-11-14 Chuyu Zhou , Tianyu Li , Chenxi Lan , Rongyu Du , Guoguo Xin , Pengyu Nan , Hangzhou Yang , Guoqing Wang , Xun Liu , Wei Li

As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great…

Machine Learning · Computer Science 2022-08-09 Zhi-Yong Zhang , Hui Zhang , Li-Sheng Zhang , Lei-Lei Guo

We develop a flexible framework based on physics-informed neural networks (PINNs) for solving boundary value problems involving minimal surfaces in curved spacetimes, with a particular emphasis on singularities and moving boundaries. By…

High Energy Physics - Theory · Physics 2025-09-17 Koji Hashimoto , Koichi Kyo , Masaki Murata , Gakuto Ogiwara , Norihiro Tanahashi

The numerical approximation of partial differential equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and…

Machine Learning · Computer Science 2025-03-19 Namgyu Kang , Jaemin Oh , Youngjoon Hong , Eunbyung Park

This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…

Machine Learning · Computer Science 2023-10-02 Sidney Besnard , Frédéric Jurie , Jalal M. Fadili

Physics-informed neural networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…

Computational Physics · Physics 2026-03-25 Guoqiang Lei , D. Exposito , Xuerui Mao

In this paper we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nano-optics technologies. In particular, we successfully…

Computational Physics · Physics 2020-04-22 Yuyao Chen , Lu Lu , George Em Karniadakis , Luca Dal Negro