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Physics-informed neural networks (PINNs) provide a flexible framework for solving forward and inverse problems governed by partial differential equations (PDEs), but standard PINN training typically relies on soft penalty formulations that…

Machine Learning · Computer Science 2026-05-12 Binghang Lu , Runyu Zhang , Changhong Mou , Na Li , Guang Lin

In this study, novel physics-informed neural network (PINN) methods for coupling neighboring support points and their derivative terms which are obtained by automatic differentiation (AD), are proposed to allow efficient training with…

Machine Learning · Computer Science 2022-12-16 Pao-Hsiung Chiu , Jian Cheng Wong , Chinchun Ooi , My Ha Dao , Yew-Soon Ong

Variational inequalities are widely applied in mechanical engineering, fluid penetration, transportation, and other fields. In this paper, a Deep Ritz method based on Physics-Informed Neural Networks (PINNs) is proposed to enhance the…

Numerical Analysis · Mathematics 2026-03-13 Qijia Zhou , Yiyang Wang , Shengyuan Deng , Chenliang Li

This paper introduces PINT (Physics-Informed Neural Time Series Models), a framework that integrates physical constraints into neural time series models to improve their ability to capture complex dynamics. We apply PINT to the ERA5…

Machine Learning · Computer Science 2025-07-18 Keonvin Park , Jisu Kim , Jaemin Seo

Physics-informed neural networks (PINNs) have been widely applied in different fields due to their effectiveness in solving partial differential equations (PDEs). However, the accuracy and efficiency of PINNs need to be considerably…

Machine Learning · Computer Science 2023-08-16 Weilong Guan , Kaihan Yang , Yinsheng Chen , Zhong Guan

Physics-informed neural networks (PINNs) are promising to replace conventional partial differential equation (PDE) solvers by offering more accurate and flexible PDE solutions. However, they are hampered by the relatively slow convergence…

Machine Learning · Computer Science 2023-05-16 Mohammad H. Taufik , Tariq Alkhalifah

The numerical approximation of partial differential equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and…

Machine Learning · Computer Science 2025-03-19 Namgyu Kang , Jaemin Oh , Youngjoon Hong , Eunbyung Park

The physics-informed neural network (PINN) is effective in solving the partial differential equation (PDE) by capturing the physics constraints as a part of the training loss function through the Automatic Differentiation (AD). This study…

Computational Physics · Physics 2022-02-17 Zixue Xiang , Wei Peng , Weien Zhou , Wen Yao

Deep learning has emerged as a powerful tool in scientific modeling, particularly for complex dynamical systems; however, accurately capturing age-structured population dynamics under policy-driven fertility changes remains a significant…

Machine Learning · Computer Science 2025-05-06 Ze Tao

Physics-informed neural networks have shown significant potential in solving partial differential equations (PDEs) across diverse scientific fields. However, their performance often deteriorates when addressing PDEs with intricate and…

Machine Learning · Computer Science 2025-02-18 Nanxi Chen , Chuanjie Cui , Rujin Ma , Airong Chen , Sifan Wang

Physics-Informed Neural Networks (PINNs) are mesh-free approaches for the numerical approximation of partial differential equations, where a neural network is trained by minimizing a loss function derived from the governing equations and…

Numerical Analysis · Mathematics 2026-04-03 Medard Govoeyi , Thomas Richter

Scientific machine learning and the advent of the Physics-Informed Neural Network (PINN) have shown high potential in their ability to solve complex differential equations. One example is the use of PINNs to solve the gravity field modeling…

Machine Learning · Computer Science 2025-02-05 John Martin , Hanspeter Schaub

Physics-Informed Neural Networks (PINNs) have become a prominent application of deep learning in scientific computation, as they are powerful approximators of solutions to nonlinear partial differential equations (PDEs). There have been…

Machine Learning · Computer Science 2023-06-01 Hwijae Son , Sung Woong Cho , Hyung Ju Hwang

This paper presents a physics-informed neural network (PINN) approach for monitoring the health of diesel engines. The aim is to evaluate the engine dynamics, identify unknown parameters in a "mean value" model, and anticipate maintenance…

Machine Learning · Computer Science 2023-08-29 Kamaljyoti Nath , Xuhui Meng , Daniel J Smith , George Em Karniadakis

Exoskeletons and rehabilitation systems have the potential to improve human strength and recovery by using adaptive human-machine interfaces. Achieving precise and responsive control in these systems depends on accurately estimating joint…

Machine Learning · Computer Science 2025-02-18 Rajnish Kumar , Anand Gupta , Suriya Prakash Muthukrishnan , Lalan Kumar , Sitikantha Roy

This study takes advantage of recent advances in machine learning to establish a physics-based data analytic platform for distributed reconstruction of mechanical properties in layered components from full waveform data. In this vein, two…

Numerical Analysis · Mathematics 2023-10-20 Yang Xu , Fatemeh Pourahmadian , Jian Song , Conglin Wang

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), owing to their mesh-free nature, offer a powerful approach for solving high-dimensional partial differential equations (PDEs) in complex geometries, including irregular domains. This capability…

Numerical Analysis · Mathematics 2025-06-06 Hanfei Zhou , Lei Shi

Concrete manufacturing projects are one of the most common ones for consulting agencies. Because of the highly non-linear dependency of input materials like ash, water, cement, superplastic, etc; with the resultant strength of concrete, it…

Machine Learning · Computer Science 2024-08-31 Sam Varghese , Rahul Anand , Gaurav Paliwal

Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem,…

Numerical Analysis · Mathematics 2024-10-21 Sidi Wu
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