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A multi-grid, single-mesh online learning framework for efficient large-scale topology optimization

delete2026-08-03
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OA
AI
K
Kangjie Li
W
Wenjing Ye *
DOI：10.1007/s00366-026-02383-5delete
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摘要

摘要

En 中文
拓扑优化（TO）的最新进展日益将机器学习技术融入其中以提升计算效率。其中，在线学习方法作为大规模TO设计的有前景方法脱颖而出。与需要预生成训练数据的离线方法不同，在线学习框架在优化过程中自适应地训练代理模型，使用早期迭代的数据。当前最先进的方法通常采用两尺度局部训练范式，机器学习模型迭代学习粗尺度灵敏度场与局部补丁内细尺度结构响应之间的映射。尽管该局部策略提升了计算可扩展性并提供隐式数据增强，但其存在局限性：排除全局结构信息往往导致映射欠定和预测精度降低，因为细尺度灵敏度本质上依赖于超出单个补丁的结构上下文。为解决此问题，我们提出多网格分解策略并将其整合到在线学习框架中。该策略分层将全局结构信息纳入局部训练补丁以增强映射唯一性。此外，我们的框架在单一网格分辨率内完全实现在线学习，绕过了昂贵的粗尺度模拟同时保持精度。我们采用傅里叶神经网络算子作为代理模型，利用其直接从空间信息中捕捉结构灵敏度模式的卓越能力。所提出的方法通过2D和3D刚度设计示例进行验证，展示了通过减少高维数值模拟实现显著的计算节省。同时研究了关键超参数对框架性能的影响。
Keyword:
Topology optimization
Multi-grid decomposition
Online learning
Fourier neural operator

期刊

Engineering with Computers 封面图
Engineering with Computers
IF:
4.9
论文数:
2.6K
被引数:
9.3K

机构

D
Department of Mechanical and Aerospace Engineering
学者数:
136
论文数: 67
被引数: 0
引用论文

引用论文

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