Center for Industrial Mathematics, University of Bremen（不来梅大学工业数学中心）；Cambridge Image Analysis, Centre for Mathematical Sciences, University of Cambridge（剑桥大学数学科学中心剑桥图像分析中心）
Sören Dittmer, David Erzmann, Henrik Harms, Peter Maass
备注：
25 pages, 10 figures, submitted to the International Journal for Numerical Methods in Engineering
本文提出 SELTO，通过基于物理的预处理与等变网络提升拓扑优化深度学习流程的样本效率，并发布两个含真实解的 TO 数据集以支持基准比较。
摘要：
深度学习（DL）的最新发展展现出其在拓扑优化（TO）中的巨大潜力。然而，尽管已有一些颇具前景的尝试，该子领域在基础方法和数据集方面仍缺乏坚实基础。我们旨在同时解决这两点。首先，我们探索基于物理的预处理和等变网络，以构建用于 TO DL 流程的样本高效组件。我们采用端到端监督训练，在大规模消融研究中对其进行评估。结果表明，样本效率和预测结果的物理正确性均得到显著提升。其次，为提高可比性并推动未来进展，我们发布了首批两个包含问题及相应真实解的 TO 数据集。
英文摘要：
Recent developments in Deep Learning (DL) suggest a vast potential for Topology Optimization (TO). However, while there are some promising attempts, the subfield still lacks a firm footing regarding basic methods and datasets. We aim to address both points. First, we explore physics-based preprocessing and equivariant networks to create sample-efficient components for TO DL pipelines. We evaluate them in a large-scale ablation study using end-to-end supervised training. The results demonstrate a drastic improvement in sample efficiency and the predictions' physical correctness. Second, to improve comparability and future progress, we publish the two first TO datasets containing problems and corresponding ground truth solutions.
Neural Networks for Generating Better Local Optima in Topology Optimization
Chair of Computational Modeling and Simulation, Technical University of Munich, School of Engineering and Design, Arcisstraße 21, Munich, 80 333, Germany（慕尼黑技术大学计算建模与模拟系）；Department of Civil and Mechanical Engineering, Technical University of Denmark（丹麦技术大学土木与机械工程系）；BMW Group, Knorrstraße 147, 80937 München（宝马集团）；Chair of Data Science in Engineering, Bauhaus-Universität Weimar, Coudraystraße 13 b, 99423, Weimar, Germany（魏玛包豪斯大学工程数据科学系）
Simplifying deflation for non-convex optimization with applications in Bayesian inference and topology optimization
Pumas-AI Inc.（Pumas-AI公司）；The University of Sydney Business School（悉尼大学商学院）；Department of Architecture, Massachusetts Institute of Technology（麻省理工学院建筑系（注：因要求机构粒度到大学级别，此处实际机构应为麻省理工学院））
University of Amsterdam, Amsterdam, The Netherlands（阿姆斯特丹大学）；Skolkovo Institute of Science and Technology（斯克沃尔诺夫科学与技术研究所）；Institute of Numerical Mathematics RAS, Moscow, Russia（俄罗斯科学院数值数学研究所）
Consistent machine learning for topology optimization with microstructure-dependent neural network material models
Delft University of Technology（代尔夫特理工大学）；Princeton University（普林斯顿大学）；Princeton Materials Institute (PMI), Princeton University（普林斯顿材料研究所（PMI），普林斯顿大学）；Brown University（布朗大学）
