English
Related papers

Related papers: Learning from Integral Losses in Physics Informed …

200 papers

Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems, but they are still trapped in training failures when the target functions to be approximated exhibit…

Machine Learning · Computer Science 2023-03-06 Ye Li , Song-Can Chen , Sheng-Jun Huang

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

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

Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what…

Machine Learning · Computer Science 2024-11-28 Emily Williams , Amanda Howard , Brek Meuris , Panos Stinis

Eigenvalue problems are critical to several fields of science and engineering. We expand on the method of using unsupervised neural networks for discovering eigenfunctions and eigenvalues for differential eigenvalue problems. The obtained…

Machine Learning · Computer Science 2022-03-02 Henry Jin , Marios Mattheakis , Pavlos Protopapas

In this paper, we introduce an innovative approach for addressing Bayesian inverse problems through the utilization of physics-informed invertible neural networks (PI-INN). The PI-INN framework encompasses two sub-networks: an invertible…

Numerical Analysis · Mathematics 2023-10-04 Xiaofei Guan , Xintong Wang , Hao Wu , Zihao Yang , Peng Yu

Physics-informed neural networks (PINNs) have been proposed to solve two main classes of problems: data-driven solutions and data-driven discovery of partial differential equations. This task becomes prohibitive when such data is highly…

Machine Learning · Computer Science 2022-10-20 Wei Peng , Wen Yao , Weien Zhou , Xiaoya Zhang , Weijie Yao

Physics-Informed Neural Networks (PINNs) have emerged as a highly active research topic across multiple disciplines in science and engineering, including computational geomechanics. PINNs offer a promising approach in different applications…

Computational Engineering, Finance, and Science · Computer Science 2024-04-30 Yared W. Bekele

Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…

Machine Learning · Computer Science 2022-03-28 Alexander Henkes , Henning Wessels , Rolf Mahnken

This paper presents the potential of applying physics-informed neural networks for solving nonlinear multiphysics problems, which are essential to many fields such as biomedical engineering, earthquake prediction, and underground energy…

Computational Engineering, Finance, and Science · Computer Science 2020-07-01 Teeratorn Kadeethum , Thomas M Jorgensen , Hamidreza M Nick

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

The concepts and techniques of physics-informed neural networks (PINNs) is studied and limitations are identified to make it efficient to approximate dynamical equations. Potential working research domains are explored for increasing the…

Computational Physics · Physics 2023-01-13 Siddharth Rout

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

Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…

Computational Physics · Physics 2019-10-31 Bing Xiong , Haiyang Fu , Feng Xu , Yaqiu Jin

The residual loss in Physics-Informed Neural Networks (PINNs) alters the simple recursive relation of layers in a feed-forward neural network by applying a differential operator, resulting in a loss landscape that is inherently different…

Machine Learning · Computer Science 2024-06-14 Nima Hosseini Dashtbayaz , Ghazal Farhani , Boyu Wang , Charles X. Ling

Physics-informed neural networks (PINNs) have been proven as a promising way for solving various partial differential equations, especially high-dimensional ones and those with irregular boundaries. However, their capabilities in real…

Dynamical Systems · Mathematics 2026-03-27 Guojie Li , Wuyue Yang , Liu Hong

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…

Physics informed neural network (PINN) based solution methods for differential equations have recently shown success in a variety of scientific computing applications. Several authors have reported difficulties, however, when using PINNs to…

Numerical Analysis · Mathematics 2023-10-16 Arnav Gangal , Luis Kim , Sean P. Carney

Learning the full family of solutions to parameterized partial differential equations (PDEs) is a central challenge to our ability to model the behavior of heterogeneous systems, with a variety of fundamental and application-oriented…

Computational Physics · Physics 2026-01-26 Milad Panahi , Giovanni Michele Porta , Monica Riva , Alberto Guadagnini

We propose the use of physics-informed neural networks for solving the shallow-water equations on the sphere in the meteorological context. Physics-informed neural networks are trained to satisfy the differential equations along with the…

Computational Physics · Physics 2024-09-19 Alex Bihlo , Roman O. Popovych