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Physics-informed neural networks (PINNs) offer a unified framework for solving both forward and inverse problems of differential equations, yet their performance and physical consistency strongly depend on how governing laws are…

Machine Learning · Computer Science 2026-03-31 Guojie Li , Liu Hong

Deep neural networks (DNNs) are powerful black-box function approximators which have been shown to yield improved performance compared to traditional neural network (NN) architectures. However, black-box algorithms do not incorporate known…

Systems and Control · Electrical Eng. & Systems 2025-10-27 Rebecca G. Hart , Wanjiku A. Makumi , Rushikesh Kamalapurkar , Warren E. Dixon

Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws…

Machine Learning · Computer Science 2025-06-09 Wenxuan Huo , Qiang He , Gang Zhu , Weifeng Huang

Deep neural networks (DNNs) are powerful tools for compressing and distilling information. Their scale and complexity, often involving billions of inter-dependent parameters, render direct microscopic analysis difficult. Under such…

Machine Learning · Statistics 2022-09-26 Inbar Seroussi , Gadi Naveh , Zohar Ringel

Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods PINNs have several advantages, for example their…

Computational Physics · Physics 2024-06-21 Ben Moseley , Andrew Markham , Tarje Nissen-Meyer

Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving…

Fluid Dynamics · Physics 2025-01-22 Jiahao Song , Wenbo Cao , Weiwei Zhang

This dissertation investigates physics-informed neural networks (PINNs) as candidate models for encoding governing equations, and assesses their performance on experimental data from two different systems. The first system is a simple…

Machine Learning · Computer Science 2024-01-09 Hamza Alsharif

Seismic wave forward and inverse modeling are fundamental tools for subsurface imaging and geological hazard assessment. Conventional grid-based numerical methods, such as finite-difference and finite-element approaches, often require dense…

Geophysics · Physics 2026-01-23 Chaohua Liang , Xingliang Peng , Jun Matsushima

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

In this paper, we introduce a physics-driven regularization method for training of deep neural networks (DNNs) for use in engineering design and analysis problems. In particular, we focus on prediction of a physical system, for which in…

Machine Learning · Computer Science 2019-10-17 Mohammad Amin Nabian , Hadi Meidani

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

We present a Physics-Informed Neural Network (PINN) to simulate the thermochemical evolution of a composite material on a tool undergoing cure in an autoclave. In particular, we solve the governing coupled system of differential equations…

Machine Learning · Computer Science 2021-06-16 Sina Amini Niaki , Ehsan Haghighat , Trevor Campbell , Anoush Poursartip , Reza Vaziri

A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…

Numerical Analysis · Mathematics 2024-01-25 Vasiliy A. Es'kin , Danil V. Davydov , Julia V. Gur'eva , Alexey O. Malkhanov , Mikhail E. Smorkalov

Traditional physics-informed neural networks (PINNs) do not always satisfy physics based constraints, especially when the constraints include differential operators. Rather, they minimize the constraint violations in a soft way. Strict…

Machine Learning · Computer Science 2025-12-08 Rahul Golder , Bimol Nath Roy , M. M. Faruque Hasan

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

In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning…

Numerical Analysis · Mathematics 2024-04-25 Pasquale Ambrosio , Salvatore Cuomo , Mariapia De Rosa

Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…

Computational Physics · Physics 2024-06-10 Michel Nohra , Steven Dufour

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

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 an ever expanding set of research and application areas, deep neural networks (DNNs) set the bar for algorithm performance. However, depending upon additional constraints such as processing power and execution time limits, or…

Machine Learning · Computer Science 2021-06-22 Nathan Dahlin , Krishna Chaitanya Kalagarla , Nikhil Naik , Rahul Jain , Pierluigi Nuzzo