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Physics-informed neural networks (PINNs) have emerged as a flexible framework for solving partial differential equations, but their performance on interface problems remains challenging because continuity and flux conditions are typically…

Numerical Analysis · Mathematics 2026-05-19 Seung Whan Chung , Stephen T. Castonguay , Sumanta Roy , Michael S. Penwarden , Yucheng Fu , Pratanu Roy

We develop improved physics-informed neural networks (PINNs) for high-order and high-dimensional power system models described by nonlinear ordinary differential equations. We propose some novel enhancements to improve PINN training and…

Machine Learning · Computer Science 2024-10-11 Vineet Jagadeesan Nair

Physics-informed neural networks (PINNs) have been proposed to solve two main classes of problems: data-driven solutions and data-driven discovery of partial differential equations. This task becomes prohibitive when such data is highly…

Machine Learning · Computer Science 2022-10-20 Wei Peng , Wen Yao , Weien Zhou , Xiaoya Zhang , Weijie Yao

Physics-Informed Neural Networks (PINNs) represent a significant advancement in Scientific Machine Learning (SciML), which integrate physical domain knowledge into an empirical loss function as soft constraints and apply existing machine…

Machine Learning · Computer Science 2024-09-18 Xiaoran Cheng , Sen Na

Physics-informed neural networks (PINNs) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs are known to be robust for smaller training sets, derive better generalization…

Machine Learning · Computer Science 2024-06-19 Birgit Hillebrecht , Benjamin Unger

Quantum state tomography (QST) faces exponential measurement requirements and noise sensitivity in multi-qubit systems, bottlenecking practical quantum technologies. We present a physics-informed neural network (PINN) framework integrating…

Quantum Physics · Physics 2025-12-17 Changchun Feng , Laifa Tao , Lin Chen

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

Evolution equations, including both ordinary differential equations (ODEs) and partial differential equations (PDEs), play a pivotal role in modeling dynamic systems. However, achieving accurate long-time integration for these equations…

Numerical Analysis · Mathematics 2026-04-23 Xiaodong Feng , Haojiong Shangguan , Tao Tang , Xiaoliang Wan

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

Physics-Informed Neural Networks (PINNs) have recently shown great promise as a way of incorporating physics-based domain knowledge, including fundamental governing equations, into neural network models for many complex engineering systems.…

Machine Learning · Computer Science 2021-05-06 Jian Cheng Wong , Chinchun Ooi , Pao-Hsiung Chiu , My Ha Dao

The accurate solution of nonlinear hyperbolic partial differential equations (PDEs) remains challenging due to steep gradients, discontinuities, and multiscale structures that make conventional solvers computationally demanding.…

Machine Learning · Computer Science 2025-12-02 Saif Ur Rehman , Wajid Yousuf

In this work, we assess the ability of physics-informed neural networks (PINNs) to solve increasingly-complex coupled ordinary differential equations (ODEs). We focus on a pair of benchmarks: discretized partial differential equations and…

Machine Learning · Statistics 2022-10-17 Alexander New , Benjamin Eng , Andrea C. Timm , Andrew S. Gearhart

Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…

Neural and Evolutionary Computing · Computer Science 2023-12-25 Siqi Chen , Bin Shan , Ye Li

Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining…

Machine Learning · Computer Science 2024-10-07 Feilong Jiang , Xiaonan Hou , Min Xia

Recent advancements in physics-informed neural networks (PINNs) and their variants have garnered substantial focus from researchers due to their effectiveness in solving both forward and inverse problems governed by differential equations.…

Machine Learning · Computer Science 2026-01-06 Shivani Saini , Ramesh Kumar Vats , Arup Kumar Sahoo

Fractional physics-informed neural networks (fPINNs) have been successfully introduced in [Pang, Lu and Karniadakis, SIAM J. Sci. Comput. 41 (2019) A2603-A2626], which observe relative errors of $10^{-3} \, \sim \, 10^{-4}$ for the…

Numerical Analysis · Mathematics 2025-05-29 Na Xue , Minghua Chen

In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology,…

Fluid Dynamics · Physics 2025-11-19 Ritik Pal , Soubhik Mukherjee , Urmi Dutta , Arghya Choudhury

Physics-informed neural networks (PINNs) have plateaued at errors of $10^{-3}$-$10^{-4}$ for fourth-order partial differential equations, creating a perceived precision ceiling that limits their adoption in engineering applications. We…

Machine Learning · Computer Science 2025-07-29 Wei Shan Lee , Chi Kiu Althina Chau , Kei Chon Sio , Kam Ian Leong

This paper introduces a Transformer-Enhanced Physics-Informed Neural Network (TE-PINN) designed for accurate quaternion-based orientation estimation in high-dynamic environments, particularly within the field of robotics. By integrating…

Robotics · Computer Science 2024-09-25 Arman Asgharpoor Golroudbari

Physics-informed neural networks (PINNs) show great advantages in solving partial differential equations. In this paper, we for the first time propose to study conformable time fractional diffusion equations by using PINNs. By solving the…

Numerical Analysis · Mathematics 2021-08-18 Yinlin Ye , Yajing Li , Hongtao Fan , Xinyi Liu , Hongbing Zhang