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This paper proposes a novel neural network framework, denoted as spectral integrated neural networks (SINNs), for resolving three-dimensional forward and inverse dynamic problems. In the SINNs, the spectral integration method is applied to…

Numerical Analysis · Mathematics 2024-01-09 Lin Qiu , Fajie Wang , Wenzhen Qu , Yan Gu , Qing-Hua Qin

Physics-informed neural networks (PINNs) have recently emerged as a novel and popular approach for solving forward and inverse problems involving partial differential equations (PDEs). However, achieving stable training and obtaining…

Fluid Dynamics · Physics 2024-05-28 Wenbo Cao , Weiwei Zhang

This paper introduces scour physics-inspired neural networks (SPINNs), a hybrid physics-data-driven framework for bridge scour prediction using deep learning. SPINNs integrate physics-based, empirical equations into deep neural networks and…

Machine Learning · Computer Science 2024-09-11 Negin Yousefpour , Bo Wang

Since their advent nearly a decade ago, physics-informed neural networks (PINNs) have been studied extensively as a novel technique for solving forward and inverse problems in physics and engineering. The neural network discretization of…

Numerical Analysis · Mathematics 2025-12-18 Conor Rowan , Kai Hampleman , Kurt Maute , Alireza Doostan

Physics-informed neural networks (PINNs) provide a powerful framework for learning governing equations of dynamical systems from data. Biologically-informed neural networks (BINNs) are a variant of PINNs that preserve the known differential…

Machine Learning · Computer Science 2026-04-21 William Lavery , Jodie A. Cochrane , Christian Olesen , Dagim S. Tadele , John T. Nardini , Sara Hamis

Deep learning methods have gained considerable interest in the numerical solution of various partial differential equations (PDEs). One particular focus is physics-informed neural networks (PINN), which integrate physical principles into…

Dynamical Systems · Mathematics 2023-12-19 Xi'an Li , Jiaxin Deng , Jinran Wu , Shaotong Zhang , Weide Li , You-Gan Wang

Partial differential equations (PDEs) provide a mathematical foundation for simulating and understanding intricate behaviors in both physical sciences and engineering. With the growing capabilities of deep learning, data$-$driven approaches…

Machine Learning · Computer Science 2025-10-14 Narayan S Iyer , Bivas Bhaumik , Ram S Iyer , Satyasaran Changdar

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by…

This paper explores the difficulties in solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach…

Machine Learning · Computer Science 2023-06-21 Shamsulhaq Basir

Physics-Informed Neural Networks (PINNs) have revolutionized solving differential equations by integrating physical laws into neural networks training. This paper explores PINNs for open-loop optimal control problems (OCPs) with incomplete…

Optimization and Control · Mathematics 2025-01-27 Alessandro Alla , Giulia Bertaglia , Elisa Calzola

This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are…

Machine Learning · Computer Science 2023-09-26 Taniya Kapoor , Hongrui Wang , Alfredo Nunez , Rolf Dollevoet

A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…

Machine Learning · Computer Science 2025-03-27 Seyedeh Azadeh Fallah Mortezanejad , Ruochen Wang , Ali Mohammad-Djafari

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…

Neural and Evolutionary Computing · Computer Science 2026-02-23 Jian Cheng Wong , Abhishek Gupta , Chin Chun Ooi , Pao-Hsiung Chiu , Jiao Liu , Yew-Soon Ong

Physics-informed neural networks (PINNs) is becoming a popular alternative method for solving partial differential equations (PDEs). However, they require dedicated manual modifications to the hyperparameters of the network, the sampling…

Computational Engineering, Finance, and Science · Computer Science 2025-04-15 Rui Zhang , Liang Li , Stéphane Lanteri , Hao Kang , Jiaqi Li

Physics-Informed Neural Networks (PINNs) have been recognized as a mesh-free alternative to solve partial differential equations where physics information is incorporated. However, in dealing with problems characterized by high stiffness or…

Machine Learning · Computer Science 2026-03-04 Divyavardhan Singh , Shubham Kamble , Dimple Sonone , Kishor Upla

Deep learning techniques with neural networks have been used effectively in computational fluid dynamics (CFD) to obtain solutions to nonlinear differential equations. This paper presents a physics-informed neural network (PINN) approach to…

Machine Learning · Computer Science 2023-07-25 Greeshma Krishna , Malavika S Nair , Pramod P Nair , Anil Lal S

Physics-Informed Neural Networks (PINNs) have recently emerged as a promising alternative for solving partial differential equations, offering a mesh-free framework that incorporates physical laws directly into the learning process. In this…

Computational Physics · Physics 2025-04-17 Gal G. Shaviner , Hemanth Chandravamsi , Shimon Pisnoy , Ziv Chen , Steven H. Frankel

In solving partial differential equations (PDEs), machine learning utilizing physical laws has received considerable attention owing to advantages such as mesh-free solutions, unsupervised learning, and feasibility for solving…

Machine Learning · Computer Science 2026-03-25 Tetsuro Tsuchino , Motoki Shiga

Physics-Informed Neural Networks (PINNs) are a class of deep neural networks that are trained, using automatic differentiation, to compute the response of systems governed by partial differential equations (PDEs). The training of PINNs is…

Machine Learning · Computer Science 2021-04-27 Mohammad Amin Nabian , Rini Jasmine Gladstone , Hadi Meidani

This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms…

Computational Physics · Physics 2024-12-16 Jorge F. Urbán , Petros Stefanou , José A. Pons