東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Nonlinear Dimension Reduction With N...

Xiong, Zeyu,

Linked to FindBook

Google Book

Amazon

博客來

Nonlinear Dimension Reduction With Neural Kernel for Path-Dependent Solid Mechanics Problems /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Nonlinear Dimension Reduction With Neural Kernel for Path-Dependent Solid Mechanics Problems // Zeyu Xiong.
Author:	Xiong, Zeyu,
Description:	1 electronic resource (144 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-08, Section: B.
Contained By:	Dissertations Abstracts International86-08B.
Subject:	Engineering. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31839930
ISBN:	9798304912143

Nonlinear Dimension Reduction With Neural Kernel for Path-Dependent Solid Mechanics Problems /
Xiong, Zeyu,

Nonlinear Dimension Reduction With Neural Kernel for Path-Dependent Solid Mechanics Problems /Zeyu Xiong. - 1 electronic resource (144 pages)

Source: Dissertations Abstracts International, Volume: 86-08, Section: B.

Data-driven modeling of the path-dependent behavior of materials with complex internal structures enables us to predict the mechanical response under time-dependent deformation through the homogenized internal failure mechanism. However, these materials present a significant modeling challenge because they require a large number of variables to capture their internal distortions, leading to higher dimensionality and increased computational costs. Hence, this dissertation aims to achieve efficient and accurate material modeling through dimension reduction. To address this challenge, we introduce the data- or node-dependent neural kernel (NK) to train a reduced number of NK basis functions that efficiently span a lower-dimensional latent space for the higher-dimensional model.One data-driven modeling approach explored is to train a surrogate micromorphic constitutive law. This approach introduces additional variables to describe the higher-order deformation of sampled materials and then examines the mechanical responses of these materials under such deformation. In this context, NK is employed to train the plastic yield function based on sampled yield stress data. With the trained yield function, the return mapping algorithm captures the path-dependent relationship between higher-order stress and deformation, or micromorphic mechanical response. Results demonstrate that the NK method surpasses the conventional multi-layer perceptron (MLP) in extrapolating sparsely distributed yield stress data, which is achieved by leveraging the span of kernel basis functions to learn data patterns more effectively.Another approach involves modeling cracked materials using fine-mesh finite element methods (FEM). Although fine-mesh FEM can approximate discontinuities caused by internal cracks, it generates large matrix equations, which makes the approach computationally intensive. To address this, a hierarchical neural kernel (HiNK) architecture is introduced, combining hierarchical deep neural networks for FEM (HiDeNN-FEM) and NK enhancement to efficiently solve discontinuous boundary value problems (BVPs). In this architecture, HiDeNN-FEM generates trainable, coarse-mesh finite element shape functions (piecewise polynomials) to approximate the continuous solution. NK enhancement is then allocated to the region of discontinuity, accurately capturing these complex features. Results indicate that HiNK basis functions efficiently characterize discontinuous BVPs, providing a powerful tool for solving high-dimensional and computationally demanding FEM models.

English

ISBN: 9798304912143Subjects--Topical Terms:

586835
Engineering.
Subjects--Index Terms:

Neural kernel

Nonlinear Dimension Reduction With Neural Kernel for Path-Dependent Solid Mechanics Problems /
LDR:04010nmm a22004453i 4500 001 2433779
005 20250905091011.5
006 m o d
007 cr|nu||||||||
008 261011s2025 miu||||||m |||||||eng d
020 $a 9798304912143
035 $a (MiAaPQD)AAI31839930
035 $a AAI31839930
040 $a MiAaPQD $b eng $c MiAaPQD $e rda
100 1 $a Xiong, Zeyu, $e author. $3 3823526
245 1 0 $a Nonlinear Dimension Reduction With Neural Kernel for Path-Dependent Solid Mechanics Problems / $c Zeyu Xiong.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (144 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 86-08, Section: B.
500 $a Advisors: Sun, WaiChing.
502 $b Ph.D. $c Columbia University $d 2025.
520 $a Data-driven modeling of the path-dependent behavior of materials with complex internal structures enables us to predict the mechanical response under time-dependent deformation through the homogenized internal failure mechanism. However, these materials present a significant modeling challenge because they require a large number of variables to capture their internal distortions, leading to higher dimensionality and increased computational costs. Hence, this dissertation aims to achieve efficient and accurate material modeling through dimension reduction. To address this challenge, we introduce the data- or node-dependent neural kernel (NK) to train a reduced number of NK basis functions that efficiently span a lower-dimensional latent space for the higher-dimensional model.One data-driven modeling approach explored is to train a surrogate micromorphic constitutive law. This approach introduces additional variables to describe the higher-order deformation of sampled materials and then examines the mechanical responses of these materials under such deformation. In this context, NK is employed to train the plastic yield function based on sampled yield stress data. With the trained yield function, the return mapping algorithm captures the path-dependent relationship between higher-order stress and deformation, or micromorphic mechanical response. Results demonstrate that the NK method surpasses the conventional multi-layer perceptron (MLP) in extrapolating sparsely distributed yield stress data, which is achieved by leveraging the span of kernel basis functions to learn data patterns more effectively.Another approach involves modeling cracked materials using fine-mesh finite element methods (FEM). Although fine-mesh FEM can approximate discontinuities caused by internal cracks, it generates large matrix equations, which makes the approach computationally intensive. To address this, a hierarchical neural kernel (HiNK) architecture is introduced, combining hierarchical deep neural networks for FEM (HiDeNN-FEM) and NK enhancement to efficiently solve discontinuous boundary value problems (BVPs). In this architecture, HiDeNN-FEM generates trainable, coarse-mesh finite element shape functions (piecewise polynomials) to approximate the continuous solution. NK enhancement is then allocated to the region of discontinuity, accurately capturing these complex features. Results indicate that HiNK basis functions efficiently characterize discontinuous BVPs, providing a powerful tool for solving high-dimensional and computationally demanding FEM models.
546 $a English
590 $a School code: 0054
650 4 $a Engineering. $3 586835
650 4 $a Materials science. $3 543314
650 4 $a Mechanics. $3 525881
650 4 $a Plastics. $3 649803
653 $a Neural kernel
653 $a Plastic yield function
653 $a Hierarchical neural kernel
653 $a Finite element methods
653 $a Boundary value problems
690 $a 0537
690 $a 0346
690 $a 0794
690 $a 0795
710 2 $a Columbia University. $b Civil Engineering and Engineering Mechanics. $e degree granting institution. $3 3815978
720 1 $a Sun, WaiChing $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-08B.
790 $a 0054
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31839930