标题： 元神经拓扑优化：元学习中的知识注入 显示英文标题

标题： Meta-neural Topology Optimization: Knowledge Infusion with Meta-learning

摘要： 工程师从他们创造的每个设计中学习，建立起有助于他们快速识别新问题有前途解决方案的直觉。 拓扑优化（TO）——一种用于设计性能优化结构的成熟计算方法——缺乏这种从经验中学习的能力。 现有方法将设计任务孤立处理，对于每个新问题都从“空白画布”设计开始，通常需要许多计算成本高昂的步骤才能收敛。 我们提出了一种元学习策略，称为元神经拓扑优化，通过在相关任务之间系统地转移知识，找到有效的初始设计，利用神经再参数化提供的与网格无关的表示。 我们将我们的方法与现有的TO方法进行比较，证明了在各种测试案例中高效优化，而不会损害设计质量。 此外，我们展示了强大的跨分辨率迁移能力，在较低分辨率离散化上学习的初始化在更高分辨率测试集上的74.1%的任务中实现了更好的收敛性，与标准神经TO相比，平均迭代次数减少了33.6%。 值得注意的是，我们发现元学习自然倾向于均匀密度设计中的应变能模式作为有效的起点，这与工程直觉一致。 显示英文摘要

摘要： Engineers learn from every design they create, building intuition that helps them quickly identify promising solutions for new problems. Topology optimization (TO) - a well-established computational method for designing structures with optimized performance - lacks this ability to learn from experience. Existing approaches treat design tasks in isolation, starting from a "blank canvas" design for each new problem, often requiring many computationally expensive steps to converge. We propose a meta-learning strategy, termed meta-neural TO, that finds effective initial designs through a systematic transfer of knowledge between related tasks, building on the mesh-agnostic representation provided by neural reparameterization. We compare our approach against established TO methods, demonstrating efficient optimization across diverse test cases without compromising design quality. Further, we demonstrate powerful cross-resolution transfer capabilities, where initializations learned on lower-resolution discretizations lead to superior convergence in 74.1% of tasks on a higher-resolution test set, reducing the average number of iterations by 33.6% compared to standard neural TO. Remarkably, we discover that meta-learning naturally gravitates toward the strain energy patterns found in uniform density designs as effective starting points, aligning with engineering intuition.