English
Related papers

Related papers: Solving the wave equation with physics-informed de…

200 papers

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs),…

Machine Learning · Computer Science 2021-11-03 Lu Lu , Xuhui Meng , Zhiping Mao , George E. Karniadakis

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

In recent years, physics-informed neural networks (PINNs) have gained significant attention for solving differential equations, although they suffer from two fundamental limitations, namely, spectral bias inherent in neural networks and…

Machine Learning · Computer Science 2026-05-01 Himanshu Pandey , Ratikanta Behera

With the advantages of fast calculating speed and high precision, the physics-informed neural network method opens up a new approach for numerically solving nonlinear partial differential equations. Based on conserved quantities, we devise…

Exactly Solvable and Integrable Systems · Physics 2022-03-14 Shuning Lin , Yong Chen

Large-scale river models are being refined over coastal regions to improve the scientific understanding of coastal processes, hazards and responses to climate change. However, coarse mesh resolutions and approximations in physical…

Fluid Dynamics · Physics 2023-03-15 Dongyu Feng , Zeli Tan , QiZhi He

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

Numerical Analysis · Mathematics 2020-06-16 Chengping Rao , Hao Sun , Yang Liu

Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and inverse problems. In the paper at hand, full waveform…

Numerical Analysis · Mathematics 2023-12-05 Leon Herrmann , Tim Bürchner , Felix Dietrich , Stefan Kollmannsberger

Turbulent fluid flows are among the most computationally demanding problems in science, requiring enormous computational resources that become prohibitive at high flow speeds. Physics-informed neural networks (PINNs) represent a radically…

Machine Learning · Computer Science 2025-10-14 Sifan Wang , Shyam Sankaran , Xiantao Fan , Panos Stinis , Paris Perdikaris

The use of deep learning in physical sciences has recently boosted the ability of researchers to tackle physical systems where little or no analytical insight is available. Recently, the Physics-Informed Neural Networks (PINNs) have been…

Quantum Physics · Physics 2024-10-23 Lorenzo Brevi , Antonio Mandarino , Enrico Prati

Machine learning techniques have proven to be effective in addressing the structure of atomic nuclei. Physics$-$Informed Neural Networks (PINNs) are a promising machine learning technique suitable for solving integro-differential problems…

Computational Physics · Physics 2026-02-13 Lorenzo Brevi , Antonio Mandarino , Carlo Barbieri , Enrico Prati

Neutrino oscillations provide crucial insights into fundamental particle physics, with two-flavor approximations effectively describing reactor and atmospheric phenomena. This paper investigates the application of Physics-Informed Neural…

High Energy Physics - Phenomenology · Physics 2026-05-14 Srinivasan T. , Kalyani Desikan

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

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) offer a powerful framework for seismic wavefield modeling, yet they typically require time-consuming retraining when applied to different velocity models. Moreover, their training can suffer from…

Geophysics · Physics 2025-06-03 Shijun Cheng , Tariq Alkhalifah

Room acoustic simulations at low frequencies often face significant uncertainties of material parameters and boundary conditions due to absorbing material. We discuss the application of Physics-Informed Neural Networks (PINNs) to solve the…

Computational Physics · Physics 2024-03-12 Stefan Schoder , Florian Kraxberger

Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed…

Machine Learning · Computer Science 2022-07-06 Shaan Desai , Marios Mattheakis , Hayden Joy , Pavlos Protopapas , Stephen Roberts

A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…

Numerical Analysis · Mathematics 2024-01-25 Vasiliy A. Es'kin , Danil V. Davydov , Julia V. Gur'eva , Alexey O. Malkhanov , Mikhail E. Smorkalov

We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN,…

Machine Learning · Computer Science 2020-05-12 Ehsan Haghighat , Maziar Raissi , Adrian Moure , Hector Gomez , Ruben Juanes

In solving partial differential equations (PDEs), machine learning utilizing physical laws has received considerable attention owing to advantages such as mesh-free solutions, unsupervised learning, and feasibility for solving…

Machine Learning · Computer Science 2026-03-25 Tetsuro Tsuchino , Motoki Shiga

Accretion disks are ubiquitous in astrophysics, appearing in diverse environments from planet-forming systems to X-ray binaries and active galactic nuclei. Traditionally, modeling their dynamics requires computationally intensive…

Earth and Planetary Astrophysics · Physics 2025-09-26 Shunyuan Mao , Weiqi Wang , Sifan Wang , Ruobing Dong , Lu Lu , Kwang Moo Yi , Paris Perdikaris , Andrea Isella , Sébastien Fabbro , Lile Wang