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Motivated by recent research on Physics-Informed Neural Networks (PINNs), we make the first attempt to introduce the PINNs for numerical simulation of the elliptic Partial Differential Equations (PDEs) on 3D manifolds. PINNs are one of the…

Numerical Analysis · Mathematics 2021-03-05 Zhuochao Tang , Zhuojia Fu

This paper proposes a meshless deep learning algorithm, enriched physics-informed neural networks (EPINNs), to solve dynamic Poisson-Nernst-Planck (PNP) equations with strong coupling and nonlinear characteristics. The EPINNs takes the…

Machine Learning · Computer Science 2024-02-06 Xujia Huang , Fajie Wang , Benrong Zhang , Hanqing Liu

Physics-informed neural networks (PINNs) have been applied to simulate multiphase flows, yet they are limited in modeling phase changes and sharp interfaces due to optimization conflicts in the strongly coupled Allen-Cahn, Cahn-Hilliard,…

Computational Physics · Physics 2026-01-22 Guoqiang Lei , Zhihua Wang , Lijing Zhou , D. Exposito , Xuerui Mao

We introduce Structure Informed Neural Networks (SINNs), a novel method for solving boundary observation problems involving PDEs. The SINN methodology is a data-driven framework for creating approximate solutions to internal variables on…

Fluid Dynamics · Physics 2023-10-31 Jakub Horsky , Andrew Wynn

Physics-Informed Neural Networks (PINNs) have become a popular and powerful framework for solving partial differential equations (PDEs), leveraging neural networks to approximate solutions while embedding PDE constraints, boundary…

Numerical Analysis · Mathematics 2026-02-03 Zijuan Xin , Chenyao Wang , Feng Shi , Yizhong Sun

We develop a new class of physics-informed neural network approximations for the stationary Oseen equations based on stability-consistent loss constructions. In contrast to standard PINN formulations, which are typically heuristic, the…

Numerical Analysis · Mathematics 2026-05-07 Shiv Mishra , Arbaz Khan

A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…

Machine Learning · Computer Science 2022-12-16 Jian Cheng Wong , Chinchun Ooi , Abhishek Gupta , Yew-Soon Ong

Physics-informed neural networks (PINNs) have emerged as a promising mesh-free paradigm for solving partial differential equations, yet adoption in science and engineering is limited by slow training and modest accuracy relative to modern…

Computational Engineering, Finance, and Science · Computer Science 2026-02-24 Pao-Hsiung Chiu , Jian Cheng Wong , Chin Chun Ooi , Chang Wei , Yuchen Fan , Yew-Soon Ong

Deep learning techniques with neural networks have been used effectively in computational fluid dynamics (CFD) to obtain solutions to nonlinear differential equations. This paper presents a physics-informed neural network (PINN) approach to…

Machine Learning · Computer Science 2023-07-25 Greeshma Krishna , Malavika S Nair , Pramod P Nair , Anil Lal S

Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training…

Fluid Dynamics · Physics 2020-11-24 Chengping Rao , Hao Sun , Yang Liu

Physics-informed neural networks (PINNs) are employed to solve the classical compressible flow problem in a converging-diverging nozzle. This problem represents a typical example described by the Euler equations, thorough understanding of…

Fluid Dynamics · Physics 2023-07-10 Liang Hong , Song Zilong , Zhao Chong , Bian Xin

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

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

Physics-informed neural networks (PINNs) are a class of deep learning models that utilize physics in the form of differential equations to address complex problems, including those with limited data availability. However, solving…

Machine Learning · Computer Science 2026-03-26 Himanshu Pandey , Anshima Singh , Ratikanta Behera

Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…

Machine Learning · Computer Science 2022-04-06 Jeremy Yu , Lu Lu , Xuhui Meng , George Em Karniadakis

Physics-informed neural networks (PINNs) have emerged as a powerful approach for solving partial differential equations (PDEs) by training neural networks with loss functions that incorporate physical constraints. In this work, we introduce…

Machine Learning · Computer Science 2026-01-29 Madison Cooley , Robert M. Kirby , Shandian Zhe , Varun Shankar

There has been an increasing interest in integrating physics knowledge and machine learning for modeling dynamical systems. However, very limited studies have been conducted on seismic wave modeling tasks. A critical challenge is that these…

Geophysics · Physics 2022-11-03 Pu Ren , Chengping Rao , Su Chen , Jian-Xun Wang , Hao Sun , Yang Liu

In this work, we present the physics-informed neural network (PINN) model applied particularly to dynamic problems in solid mechanics. We focus on forward and inverse problems. Particularly, we show how a PINN model can be used efficiently…

Neural and Evolutionary Computing · Computer Science 2025-12-16 Vijay Kag , Venkatesh Gopinath

In this paper, a meshfree method using physics-informed neural networks (PINNs) is developed for solving two-phase flow problems with moving interfaces, where two immiscible fluids bearing different material properties, are separated by a…

Numerical Analysis · Mathematics 2026-04-02 Qijia Zhai , Pengtao Sun , Xiaoping Xie , Xingwen Zhu , Chen-Song Zhang

The electromagnetic inverse scattering problem (ISP), due to its inherent strong nonlinearity and severe ill-posedness, has long been a core challenge in microwave imaging. In recent years, physics-informed neural networks (PINNs) have…

Signal Processing · Electrical Eng. & Systems 2026-05-05 Shilong Sun