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Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…

Machine Learning · Computer Science 2022-11-02 Raphaël Pellegrin , Blake Bullwinkel , Marios Mattheakis , Pavlos Protopapas

Partial differential equations (PDEs) provide a mathematical foundation for simulating and understanding intricate behaviors in both physical sciences and engineering. With the growing capabilities of deep learning, data$-$driven approaches…

Machine Learning · Computer Science 2025-10-14 Narayan S Iyer , Bivas Bhaumik , Ram S Iyer , Satyasaran Changdar

Since the introduction of deep learning for solving partial differential equations (PDEs), there has been growing interest in real-time system responses, where the kernel function plays a key role. Physics-informed neural networks (PINNs),…

Numerical Analysis · Mathematics 2025-11-17 Xiaopei Jiao , Fansheng Xiong

Physics-Informed Neural Networks (PINNs) have become a prominent application of deep learning in scientific computation, as they are powerful approximators of solutions to nonlinear partial differential equations (PDEs). There have been…

Machine Learning · Computer Science 2023-06-01 Hwijae Son , Sung Woong Cho , Hyung Ju Hwang

Temporally and spatially dependent uncertain parameters are regularly encountered in engineering applications. Commonly these uncertainties are accounted for using random fields and processes, which require knowledge about the appearing…

Numerical Analysis · Mathematics 2021-11-23 Jan Niklas Fuhg , Ioannis Kalogeris , Amélie Fau , Nikolaos Bouklas

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…

Numerical Analysis · Mathematics 2024-11-20 Tim De Ryck , Siddhartha Mishra

Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) from a variety of experimental perspectives. Some recent studies have also proposed PINN algorithms for PDEs on…

Numerical Analysis · Mathematics 2024-08-06 Guanhang Lei , Zhen Lei , Lei Shi , Chenyu Zeng , Ding-Xuan Zhou

Physics-Informed Neural Networks (PINNs) have enabled significant improvements in modelling physical processes described by partial differential equations (PDEs). PINNs are based on simple architectures, and learn the behavior of complex…

We consider the approximation of a class of dynamic partial differential equations (PDE) of second order in time by the physics-informed neural network (PINN) approach, and provide an error analysis of PINN for the wave equation, the…

Numerical Analysis · Mathematics 2023-03-23 Yanxia Qian , Yongchao Zhang , Yunqing Huang , Suchuan Dong

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) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs are known to be robust for smaller training sets, derive better generalization…

Machine Learning · Computer Science 2024-06-19 Birgit Hillebrecht , Benjamin Unger

Physically informed neural networks (PINNs) are a promising emerging method for solving differential equations. As in many other deep learning approaches, the choice of PINN design and training protocol requires careful craftsmanship. Here,…

Machine Learning · Statistics 2023-10-09 Inbar Seroussi , Asaf Miron , Zohar Ringel

Physics-informed neural networks (PINNs) provide a powerful framework for learning governing equations of dynamical systems from data. Biologically-informed neural networks (BINNs) are a variant of PINNs that preserve the known differential…

Machine Learning · Computer Science 2026-04-21 William Lavery , Jodie A. Cochrane , Christian Olesen , Dagim S. Tadele , John T. Nardini , Sara Hamis

Large-scale dynamics of the oceans and the atmosphere are governed by primitive equations (PEs). Due to the nonlinearity and nonlocality, the numerical study of the PEs is generally challenging. Neural networks have been shown to be a…

Numerical Analysis · Mathematics 2023-03-21 Ruimeng Hu , Quyuan Lin , Alan Raydan , Sui Tang

The research in Artificial Intelligence methods with potential applications in science has become an essential task in the scientific community last years. Physics Informed Neural Networks (PINNs) is one of this methods and represent a…

Computational Physics · Physics 2023-07-24 Luis Medrano Navarro , Luis Martín Moreno , Sergio G Rodrigo

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

Many physical and engineering systems require solving direct problems to predict behavior and inverse problems to determine unknown parameters from measurement. In this work, we study both aspects for systems governed by differential…

Numerical Analysis · Mathematics 2026-03-04 Noura Al Helwani , Sophie Moufawad , Georges Sakr

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) have emerged as an effective technique for solving PDEs in a wide range of domains. It is noticed, however, the performance of PINNs can vary dramatically with different sampling procedures. For…

Numerical Analysis · Mathematics 2023-01-18 Zhiwei Gao , Liang Yan , Tao Zhou

Physics-informed neural networks (PINNs) have been widely applied in different fields due to their effectiveness in solving partial differential equations (PDEs). However, the accuracy and efficiency of PINNs need to be considerably…

Machine Learning · Computer Science 2023-08-16 Weilong Guan , Kaihan Yang , Yinsheng Chen , Zhong Guan