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Application of Machine Learning and Deep Learning in Finite Element Analysis: A Comprehensive Review

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Abstract

Machine learning (ML) has evolved as a technology used in even broader domains, ranging from spam detection to space exploration, as a result of the boom in available data and affordable computing power in recent years. To find field variables in a domain under investigation, partial differential equations (PDEs) are solved using the numerical method known as finite element method (FEM). Problems in a variety of fields, including solid and fluid mechanics, material science, biomechanics, electronics, and geomechanics, have been solved using FEM. There are initiatives to apply ML approaches to the field of finite element analysis (FEA) due to the broad applicability of ML to numerous fields. The field of FEA is constrained by the length of time needed for modeling, the expense and length of time required for computing to solve the problem, and the necessity of considerable expert participation to understand the findings. These problems are frequently solved using ML approaches, according to evidence from ML applications. This work provides a thorough analysis of how ML has been applied in solid mechanics as an additional and beneficial tool to FEA. The goal is to demonstrate ML’s effectiveness in the FEA sector and to pinpoint areas that might use improvement.

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Abbreviations

AI:

Artificial intelligence

ANN:

Artificial neural network

CNN:

Convolutional neural network

CAI:

Compression-after-impact

CFRP:

Carbon fiber reinforced polymer

CNT:

Carbon nanotube

CFST:

Concrete-filled steel tubular

ERA:

Explosive reactive armour

DGM:

Deep Galerkin method

DL:

Deep learning

DNN:

Deep neural network

FE:

Finite element

FEA:

Finite element analysis

FEM:

Finite element method

GAN:

Generative adversarial network

GNN:

Graph neural network

KNN:

K-nearest neighbor

LSTM:

Long short-term memory

ML:

Machine learning

MLMM:

Machine learning material model

NURBS:

Non-uniform rational B-spline

ODE:

Ordinary differential equation

PDE:

Partial differential equation

PINN:

Physics informed neural network

RNN:

Recurrent neural network

RVE:

Representative volume element

SHM:

Structural health monitoring

SVM:

Support vector machine

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Acknowledgements

The authors gratefully acknowledge the support from SERB, DST under the projects IMP/2019/000276, CRG/2022/002218 and VSSC, ISRO through MoU No.: ISRO:2020:MOU: NO:480.

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  1. Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

    Dipjyoti Nath,  Ankit & Sachin Singh Gautam

  2. Mehta Family School of Data Science and Artificial Intelligence, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

    Debanga Raj Neog

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Nath, D., Ankit, Neog, D.R. et al. Application of Machine Learning and Deep Learning in Finite Element Analysis: A Comprehensive Review. Arch Computat Methods Eng (2024). https://doi.org/10.1007/s11831-024-10063-0

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