Applications of scientific machine learning for the analysis of functionally graded porous beams

verfasst von

Mohammad Sadegh Eshaghi, Mostafa Bamdad, Cosmin Anitescu, Yizheng Wang, Xiaoying Zhuang, Timon Rabczuk

Abstract

This study help investigates different Scientific Machine Learning (SciML) approaches for the analysis of functionally graded (FG) porous beams and compares them under a new framework. The beam material properties are assumed to vary as an arbitrary continuous function. The methods consider the output of a neural network/operator as an approximation to the displacement fields and derive the equations governing beam behavior based on the continuum formulation. They are implemented in the framework and formulated by three approaches: (a) the vector approach leads to a Physics-Informed Neural Network (PINN), (b) the energy approach brings about the Deep Energy Method (DEM), and (c) the data-driven approach, which results in a class of Neural Operator methods. Finally, a neural operator has been trained to predict the response of the porous beam with functionally graded material under any porosity distribution pattern and any arbitrary traction condition. The results are validated with analytical and numerical reference solutions. The data and code accompanying this manuscript will be publicly available at github.com/eshaghi-ms/DeepNetBeam.

Organisationseinheit(en)

Institut für Photonik

Externe Organisation(en)

Bauhaus-Universität Weimar
Tsinghua University
Tongji University

Typ

Artikel

Journal

NEUROCOMPUTING

Band

619

Anzahl der Seiten

ISSN

0925-2312

Publikationsdatum

28.02.2025

Publikationsstatus

Veröffentlicht

Peer-reviewed

ASJC Scopus Sachgebiete

Angewandte Informatik, Kognitive Neurowissenschaft, Artificial intelligence

Elektronische Version(en)

https://doi.org/10.48550/arXiv.2408.02698 (Zugang: Offen)
https://doi.org/10.1016/j.neucom.2024.129119 (Zugang: Offen)

BibTeX

@article{01497b314c774992ad1b5c3679252603,
title = "Applications of scientific machine learning for the analysis of functionally graded porous beams",
abstract = "This study help investigates different Scientific Machine Learning (SciML) approaches for the analysis of functionally graded (FG) porous beams and compares them under a new framework. The beam material properties are assumed to vary as an arbitrary continuous function. The methods consider the output of a neural network/operator as an approximation to the displacement fields and derive the equations governing beam behavior based on the continuum formulation. They are implemented in the framework and formulated by three approaches: (a) the vector approach leads to a Physics-Informed Neural Network (PINN), (b) the energy approach brings about the Deep Energy Method (DEM), and (c) the data-driven approach, which results in a class of Neural Operator methods. Finally, a neural operator has been trained to predict the response of the porous beam with functionally graded material under any porosity distribution pattern and any arbitrary traction condition. The results are validated with analytical and numerical reference solutions. The data and code accompanying this manuscript will be publicly available at https://github.com/eshaghi-ms/DeepNetBeam.",
keywords = "Deep energy method, Fourier neural operator, Functionally graded material, Physics-informed neural network, Porous beam, Scientific machine learning",
author = "Eshaghi, {Mohammad Sadegh} and Mostafa Bamdad and Cosmin Anitescu and Yizheng Wang and Xiaoying Zhuang and Timon Rabczuk",
note = "Publisher Copyright: {\textcopyright} 2024 The Authors",
year = "2025",
month = feb,
day = "28",
doi = "10.48550/arXiv.2408.02698",
language = "English",
volume = "619",
journal = "NEUROCOMPUTING",
issn = "0925-2312",
publisher = "Elsevier",
}