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We propose a hybrid solver that fuses the dimensionality-reduction strengths of the Method of Lines (MOL) with the flexibility of Physics-Informed Neural Networks (PINNs). Instead of approximating spatial derivatives with fixed…

Computational Physics · Physics 2025-12-24 Maximilian Cederholm , Siyao Wang , Haochun Wang , Ruichen Xu , Yuefan Deng

Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space--time PINNs take…

Machine Learning · Computer Science 2026-01-29 Chen-Yang Dai , Che-Chia Chang , Te-Sheng Lin , Ming-Chih Lai , Chieh-Hsin Lai

In this study, the capabilities of the Physics-Informed Neural Network (PINN) method are investigated for three major tasks: modeling, simulation, and optimization in the context of the heat conduction problem. In the modeling phase, the…

Computational Physics · Physics 2025-10-31 Ehsan Ghaderi , Mohamad Ali Bijarchi , Siamak Kazemzadeh Hannani , Ali Nouri Boroujerdi

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

Physics-informed neural networks (PINNs) have been popularized as a deep learning framework that can seamlessly synthesize observational data and partial differential equation (PDE) constraints. Their practical effectiveness however can be…

Machine Learning · Computer Science 2023-08-17 Sifan Wang , Shyam Sankaran , Hanwen Wang , Paris Perdikaris

Physics-Informed Neural Networks (PINNs) have emerged as a promising computational framework for solving differential equations by integrating deep learning with physical constraints. However, their application in gas turbines is still in…

Computational Engineering, Finance, and Science · Computer Science 2025-06-25 Afila Ajithkumar Sophiya , Sepehr Maleki , Giuseppe Bruni , Senthil K. Krishnababu

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

With the rapid advancement of graphical processing units, Physics-Informed Neural Networks (PINNs) are emerging as a promising tool for solving partial differential equations (PDEs). However, PINNs are not well suited for solving PDEs with…

Machine Learning · Computer Science 2024-05-28 Yuxiang Gao , Soheil Kolouri , Ravindra Duddu

In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design…

Machine Learning · Computer Science 2023-10-17 Woojin Cho , Kookjin Lee , Donsub Rim , Noseong Park

A Physics-Informed Neural Network (PINN) provides a distinct advantage by synergizing neural networks' capabilities with the problem's governing physical laws. In this study, we introduce an innovative approach for solving seepage problems…

Computational Engineering, Finance, and Science · Computer Science 2023-11-28 Tianfu Luo , Yelin Feng , Qingfu Huang , Zongliang Zhang , Mingjiao Yan , Zaihong Yang , Dawei Zheng , Yang Yang

In this work, we propose a learning method for solving the linear transport equation under the diffusive scaling. Due to the multiscale nature of our model equation, the model is challenging to solve by using conventional methods. We employ…

Numerical Analysis · Mathematics 2021-02-25 Liu Liu , Tieyong Zeng , Zecheng 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

The Physics-Informed Neural Network (PINN) framework introduced recently incorporates physics into deep learning, and offers a promising avenue for the solution of partial differential equations (PDEs) as well as identification of the…

Machine Learning · Computer Science 2021-08-04 Ehsan Haghighat , Ali Can Bekar , Erdogan Madenci , Ruben Juanes

A physics-informed neural network (PINN), which has been recently proposed by Raissi et al [J. Comp. Phys. 378, pp. 686-707 (2019)], is applied to the partial differential equation (PDE) of liquid film flows. The PDE considered is the time…

Physics-Informed Neural Networks (PINNs) represent a groundbreaking paradigm in scientific computing, seamlessly integrating the robust framework of deep learning with fundamental physical laws. This paper meticulously applies the standard…

Numerical Analysis · Mathematics 2026-01-19 Ahmed Aberqi , Ahmed Miloudi

Physics-informed neural networks (PINNs) constitute a flexible deep learning approach for solving partial differential equations (PDEs), which model phenomena ranging from heat conduction to quantum mechanical systems. Despite their…

Machine Learning · Computer Science 2026-03-17 Aleksander Krasowski , René P. Klausen , Aycan Celik , Sebastian Lapuschkin , Wojciech Samek , Jonas Naujoks

Physics-informed neural networks (PINNs), rooted in deep learning, have emerged as a promising approach for solving partial differential equations (PDEs). By embedding the physical information described by PDEs into feedforward neural…

Machine Learning · Computer Science 2024-01-26 Yanzhi Liu , Ruifan Wu , Ying Jiang

Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world. At least two challenges exist for PINNs at…

Computational Physics · Physics 2023-01-23 Michael Penwarden , Shandian Zhe , Akil Narayan , Robert M. Kirby

Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on…

Machine Learning · Computer Science 2025-12-11 Jinming Lu , Jiayi Tian , Yequan Zhao , Hai Li , Zheng Zhang

As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…

Machine Learning · Computer Science 2021-11-11 Yuhao Huang