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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

Physics--informed neural networks (PINN) have shown their potential in solving both direct and inverse problems of partial differential equations. In this paper, we introduce a PINN-based deep learning approach to reconstruct…

Computational Engineering, Finance, and Science · Computer Science 2024-04-24 Yuxuan Chen , Ce Wang , Yuan Hui , Mark Spivack

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

Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…

Machine Learning · Computer Science 2023-07-11 Rajat Arora

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

I will demonstrate the effectiveness of Physics-Informed Neural Networks (PINNs) in solving partial differential equations (PDEs) when training data are scarce or noisy. The training data can be located either at the boundaries or within…

Solar and Stellar Astrophysics · Physics 2025-02-28 Hubert Baty

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

Physics-informed neural networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…

Computational Physics · Physics 2026-03-25 Guoqiang Lei , D. Exposito , Xuerui Mao

Physics-informed neural networks have been widely applied to learn general parametric solutions of differential equations. Here, we propose a neural network to discover parametric eigenvalue and eigenfunction surfaces of quantum systems. We…

Machine Learning · Computer Science 2022-11-22 Marios Mattheakis , Gabriel R. Schleder , Daniel T. Larson , Efthimios Kaxiras

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

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

Physics-informed neural networks (PINNs) have recently emerged as a promising way to compute the solutions of partial differential equations (PDEs) using deep neural networks. However, despite their significant success in various fields, it…

Numerical Analysis · Mathematics 2024-07-15 Seungchan Ko , Sang Hyeon Park

The Vlasov-Poisson system is employed in its reduced form version (1D1V) as a test bed for the applicability of Physics Informed Neural Network (PINN) to the wave-particle resonance. Two examples are explored: the Landau damping and the…

Computational Physics · Physics 2023-08-25 Jai Kumar , David Zarzoso , Virginie Grandgirard , Jan Ebert , Stefan Kesselheim

Physics-informed neural networks (PINNs) in energy form, also known as the deep energy method (DEM), offer advantages over strong-form PINNs such as lower-order derivatives and fewer hyperparameters, yet dedicated and user-friendly software…

Numerical Analysis · Mathematics 2026-02-10 Yizheng Wang , Cosmin Anitescu , Mohammad Sadegh Eshaghi , Xiaoying Zhuang , Timon Rabczuk , Yinghua Liu

The present study investigates the dynamics of nonlocal beams by establishing a consistent stress-driven integral elastic using the Physics-Informed Neural Network (PINN) approach. Specifically, a PINN is developed to compute the first…

Classical Physics · Physics 2026-01-16 Baidehi Das , Raffaele Barretta , Marko Čanađija

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training. However, traditional PINN models are typically designed…

Machine Learning · Computer Science 2025-05-05 Keon Vin Park

Physics-informed neural networks (PINNs) and hybrid quantum-classical extensions provide a promising framework for solving partial differential equations (PDEs) by embedding physical laws directly into the learning process. In this work, we…

Quantum Physics · Physics 2026-02-11 Ban Q. Tran , Nahid Binandeh Dehaghani , A. Pedro Aguiar , Rafal Wisniewski , Susan Mengel

A physics-informed neural network (PINN) that combines deep learning with physics is studied to solve the nonlinear Schr\"odinger equation for learning nonlinear dynamics in fiber optics. We carry out a systematic investigation and…

Optics · Physics 2021-09-03 Xiaotian Jiang , Danshi Wang , Qirui Fan , Min Zhang , Chao Lu , Alan Pak Tao Lau

As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great…

Machine Learning · Computer Science 2022-08-09 Zhi-Yong Zhang , Hui Zhang , Li-Sheng Zhang , Lei-Lei Guo

Recently, Physics-Informed Neural Networks (PINNs) have gained significant attention for their versatile interpolation capabilities in solving partial differential equations (PDEs). Despite their potential, the training can be…

Geophysics · Physics 2024-04-12 Tariq Alkhalifah , Xinquan Huang