理论辅助的弹塑性本构关系小样本深度学习

王琛; 何有泉; 宋凌寒; 樊健生

doi:10.6052/j.issn.1000-4750.2021.12.1012

理论辅助的弹塑性本构关系小样本深度学习

doi: 10.6052/j.issn.1000-4750.2021.12.1012

王琛^1,,
何有泉^1,,
宋凌寒^1,,
樊健生^{1, 2, ,}

1.
清华大学土木工程系，北京 100084
2.
清华大学土木工程安全与耐久教育部重点实验室，北京 100084

基金项目: 国家杰出青年科学基金项目(51725803)

详细信息

作者简介:
王　琛(1993−)，男，浙江人，博士，主要从事结构工程研究(E-mail: qtwjy309@163.com)

何有泉(2002−)，男，河北人，本科生，主要从事结构工程研究(E-mail: he-yq19@mails.tsinghua.edu.cn)

宋凌寒(1997−)，男，福建人，博士生，主要从事结构工程研究(E-mail: songlh19@mails.tsinghua.edu.cn)

通讯作者:
樊健生(1975−)，男，山东人，教授，博士，主要从事结构工程研究(E-mail: fanjsh@tsinghua.edu.cn)

中图分类号: TU501
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- 被引次数: 0
出版历程
- 收稿日期: 2021-12-27
- 修回日期: 2022-06-09
- 录用日期: 2022-06-24
- 网络出版日期: 2022-06-24
- 刊出日期: 2023-09-06

A THEORY-AIDED FEW-SHOT DEEP LEARNING ALGORITHM FOR ELASTOPLASTIC CONSTITUTIVE RELATIONSHIPS

WANG Chen^1
,,
HE You-quan^1
,,
SONG Ling-han^1
,,
FAN Jian-sheng^{1, 2
, ,}

1.
Department of Civil Engineering, Tsinghua University, Beijing 100084, China
2.
Key Laboratory of Civil Engineering Safety and Durability of the Ministry of Education, Tsinghua University, Beijing 100084, China

摘要

摘要: 该文提出了一种引入经典弹塑性力学理论知识作为辅助驱动的小样本深度学习算法，适用于土木工程任意材料弹塑性本构关系，能够有效缓解大规模深度学习模型实际应用时常见的数据量匮乏瓶颈。该文简要概述了通用的经典弹塑性力学框架；在此基础上详细阐释了将弹塑性力学方程引入到常规深度学习模型中的方法与流程，该过程无需关心底层理论本构模型的具体形式与传统的复杂数值实现，保留了数据驱动技术简单、直接、高效的优点；为缓解优化目标复杂化所导致的训练不收敛问题，提出了一种与理论辅助驱动相适应的训练策略“过拟合-修正法”，能够稳定并加速收敛过程；基于结构钢材精细弹塑性本构模型开展了数值试验，验证了理论辅助的小样本学习算法的有效性，能够实现大规模深度学习模型在少量训练样本情形下获得优异的泛化性，相较纯粹数据驱动模型准确性提升38.9%。该文采用的理论辅助思想具有可借鉴性，后续可应用于结构层次的深度学习代理模型研究，促进未来更为先进、大型的智能算法落地土木工程计算领域。
- 深度学习 /
- 理论驱动 /
- 小样本学习 /
- 弹塑性本构 /
- 土木工程材料
Abstract: Proposed is a theory-aided few-shot learning algorithm applicable to any material elastoplastic relationships utilized in civil engineering. The new algorithm can effectively alleviate the paucity of data in real applications when applying large-scale deep learning models. The framework of the classical elastoplasticity theory is briefly recapped. On this basis, the paper elaborates on how to incorporate the elastoplastic equations into the ordinary deep learning models, wherein the entire processes require neither the concrete form of the underlying models nor its complicated numerical implementation, thus maintaining the simple, direct, and efficient advantages of data-driven techniques. To address the divergence issue caused by the complicated optimization target, a novel training strategy named overfitting-correction method is invented, which is able to stabilize the training and accelerate the convergence. A numerical experiment is performed upon a sophisticated elastoplastic constitutive model of structural steel. The results demonstrate that the theory-aided few-shot learning algorithm succeeds in realizing excellent generalization performance of a large-scale deep learning model on small training datasets. Quantitatively, the new algorithm overwhelms the pure data-driven model by 38.9%. The philosophy of theory-aided driven mode proposed can extend to the structural level in the future, facilitating the introduction of more advanced intelligent technologies into civil engineering.
- deep learning /
- theory-aided driven /
- few-shot learning /
- elastoplastic relationship /
- construction material

HTML全文

图 1 理论辅助的小样本学习算法

Figure 1. Theory-aided few-shot learning scheme

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图 2 数值试验采用的深度学习模型

Figure 2. The deep learning model adopted in the numerical experiment

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图 3 数据集构成示例

Figure 3. Examples of the dataset

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图 4 理论辅助的小样本学习算法模拟结果

Figure 4. Simulation results of the theory-aided few-shot learning

下载: 全尺寸图片幻灯片

图 5 理论辅助驱动模型与纯粹数据驱动模型模拟结果对比

Figure 5. Comparison of the simulation results between the theory-aided model and the pure data-driven model

下载: 全尺寸图片幻灯片

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