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A neural network-augmented patch adaptive meshless method for 3D solid mechanics.

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Title: A neural network-augmented patch adaptive meshless method for 3D solid mechanics.
Authors: Wen, Ziming1 (AUTHOR), Wang, Hu1,2 (AUTHOR) wanghu@szari.ac.cn, Yin, Jichao1 (AUTHOR), Jiang, Xinchao1 (AUTHOR), Wang, Xin1 (AUTHOR), Li, Guangyao2 (AUTHOR) liguangyao@szari.ac.cn
Source: Computational Mechanics. Jul2026, Vol. 78 Issue 1, p257-319. 63p.
Subjects: Meshfree methods, Solid mechanics, Artificial neural networks, Three-dimensional modeling, Elasticity, Numerical analysis, Elastoplasticity
Abstract: Meshless methods have achieved considerable success in solid mechanics by effectively handling large deformations and enabling adaptive refinement without the need for mesh generation. However, their convergence and accuracy can be sensitive to patch configurations and local approximations, typically requiring problem-specific tuning. While recent advanced neural network-based solvers offer a promising alternative, they may still struggle to accurately capture local features in complex domains. This study introduces a neural network-augmented meshless method for solid mechanics. Specifically, light-weight neural networks are employed for adaptive patch shape description and local weight functions within an energy-based training scheme. Furthermore, nodal enhanced neural network bases are introduced as local approximations to capture local mechanical behaviors accurately. To validate the proposed method, various three-dimensional numerical examples in linear elasticity, hyperelasticity, and elastoplasticity are presented. The comparative results indicate that the proposed framework achieves higher accuracy and faster convergence with limited network parameters and solution iterations. [ABSTRACT FROM AUTHOR]
Copyright of Computational Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: A neural network-augmented patch adaptive meshless method for 3D solid mechanics.
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  Data: <searchLink fieldCode="JN" term="%22Computational+Mechanics%22">Computational Mechanics</searchLink>. Jul2026, Vol. 78 Issue 1, p257-319. 63p.
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  Data: <searchLink fieldCode="DE" term="%22Meshfree+methods%22">Meshfree methods</searchLink><br /><searchLink fieldCode="DE" term="%22Solid+mechanics%22">Solid mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Artificial+neural+networks%22">Artificial neural networks</searchLink><br /><searchLink fieldCode="DE" term="%22Three-dimensional+modeling%22">Three-dimensional modeling</searchLink><br /><searchLink fieldCode="DE" term="%22Elasticity%22">Elasticity</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Elastoplasticity%22">Elastoplasticity</searchLink>
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  Data: Meshless methods have achieved considerable success in solid mechanics by effectively handling large deformations and enabling adaptive refinement without the need for mesh generation. However, their convergence and accuracy can be sensitive to patch configurations and local approximations, typically requiring problem-specific tuning. While recent advanced neural network-based solvers offer a promising alternative, they may still struggle to accurately capture local features in complex domains. This study introduces a neural network-augmented meshless method for solid mechanics. Specifically, light-weight neural networks are employed for adaptive patch shape description and local weight functions within an energy-based training scheme. Furthermore, nodal enhanced neural network bases are introduced as local approximations to capture local mechanical behaviors accurately. To validate the proposed method, various three-dimensional numerical examples in linear elasticity, hyperelasticity, and elastoplasticity are presented. The comparative results indicate that the proposed framework achieves higher accuracy and faster convergence with limited network parameters and solution iterations. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computational Mechanics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1007/s00466-026-02756-z
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      – Code: eng
        Text: English
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        PageCount: 63
        StartPage: 257
    Subjects:
      – SubjectFull: Meshfree methods
        Type: general
      – SubjectFull: Solid mechanics
        Type: general
      – SubjectFull: Artificial neural networks
        Type: general
      – SubjectFull: Three-dimensional modeling
        Type: general
      – SubjectFull: Elasticity
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      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Elastoplasticity
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      – TitleFull: A neural network-augmented patch adaptive meshless method for 3D solid mechanics.
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            NameFull: Wen, Ziming
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            NameFull: Jiang, Xinchao
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            NameFull: Wang, Xin
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            – D: 01
              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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              Value: 78
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