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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 attracted attention as an alternative approach to solve partial differential equations using a deep neural network (DNN). Their simplicity and capability allow them to solve inverse problems for…

Fluid Dynamics · Physics 2025-12-24 Ryuta Takao , Satoshi Ii

In this paper, we propose a cusp-capturing physics-informed neural network (PINN) to solve discontinuous-coefficient elliptic interface problems whose solution is continuous but has discontinuous first derivatives on the interface. To find…

Numerical Analysis · Mathematics 2023-08-09 Yu-Hau Tseng , Te-Sheng Lin , Wei-Fan Hu , Ming-Chih Lai

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

We proposed the boundary-integral type neural networks (BINN) for the boundary value problems in computational mechanics. The boundary integral equations are employed to transfer all the unknowns to the boundary, then the unknowns are…

Machine Learning · Computer Science 2023-05-26 Jia Sun , Yinghua Liu , Yizheng Wang , Zhenhan Yao , Xiaoping Zheng

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional…

We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale,…

Computational Physics · Physics 2020-06-23 Ben Moseley , Andrew Markham , Tarje Nissen-Meyer

Physics-informed neural networks (PINNs) have recently become a new popular method for solving forward and inverse problems governed by partial differential equations (PDEs). However, in the flow around airfoils, the fluid is greatly…

Fluid Dynamics · Physics 2024-02-26 Wenbo Cao , Jiahao Song , Weiwei Zhang

Partial differential equations (PDEs) on surfaces are fundamental to scientific computing and geometry processing. A popular approach to solving PDEs on surfaces is the finite element method (FEM), where the surface is divided into discrete…

Graphics · Computer Science 2026-05-27 Pranav Jain , Navami Kairanda , Peter Yichen Chen , Oded Stein

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

Machine Learning · Computer Science 2025-03-25 Edgar Torres , Jonathan Schiefer , Mathias Niepert

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

Recently developed physics-informed neural network (PINN) has achieved success in many science and engineering disciplines by encoding physics laws into the loss functions of the neural network, such that the network not only conforms to…

Numerical Analysis · Mathematics 2021-11-17 Weiqi Ji , Weilun Qiu , Zhiyu Shi , Shaowu Pan , Sili Deng

The potential of learned models for fundamental scientific research and discovery is drawing increasing attention worldwide. Physics-informed neural networks (PINNs), where the loss function directly embeds governing equations of scientific…

Neural and Evolutionary Computing · Computer Science 2023-12-07 Nicholas Sung Wei Yong , Jian Cheng Wong , Pao-Hsiung Chiu , Abhishek Gupta , Chinchun Ooi , Yew-Soon Ong

We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…

Machine Learning · Computer Science 2023-04-05 Hubert Baty , Leo Baty

Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, ensuring that such frameworks fully…

Machine Learning · Computer Science 2025-12-12 Nanxi Chen , Sifan Wang , Rujin Ma , Airong Chen , Chuanjie Cui

Physics-Informed Neural Networks (PINNs) are a powerful class of numerical solvers for partial differential equations, employing deep neural networks with successful applications across a diverse set of problems. However, their…

Numerical Analysis · Mathematics 2024-04-18 Tianhao Hu , Bangti Jin , Zhi Zhou

The Saint-Venant torsion theory is a classical theory for analyzing the torsional behavior of structural components, and it remains critically important in modern computational design workflows. Conventional numerical methods, including the…

Machine Learning · Computer Science 2025-05-20 Su Yeong Jo , Sanghyeon Park , Seungchan Ko , Jongcheon Park , Hosung Kim , Sangseung Lee , Joongoo Jeon

The development of biophysical models for clinical applications is rapidly advancing in the research community, thanks to their predictive nature and their ability to assist the interpretation of clinical data. However, high-resolution and…

We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the…

Machine Learning · Statistics 2019-07-08 Somdatta Goswami , Cosmin Anitescu , Souvik Chakraborty , Timon Rabczuk

Physics-informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering…

Computational Engineering, Finance, and Science · Computer Science 2022-10-05 Shahed Rezaei , Ali Harandi , Ahmad Moeineddin , Bai-Xiang Xu , Stefanie Reese