用敏感度条件流匹配提升拓扑优化的泛化能力,解决分布外性能不稳问题。
On the Generalization in Topology Optimization via Sensitivity-Conditioned Bernoulli Flow Matching

- 以敏感度为条件信号,构建流匹配生成器,提升拓扑预测精度。
- 在负载与边界条件变化下,敏感度条件使性能优于现有方法。
- 揭示物理场中哪些可近似敏感度,指导高效建模设计。
拓扑优化(TO)的代理模型在负载或边界条件变化等分布外(OOD)场景下表现不稳定,但其原因尚不明确。我们假设OOD性能取决于条件信号对驱动经典拓扑优化的伴随敏感度(即降维梯度)保留的信息量。将TO流程建模为因果马尔可夫链,数据处理不等式表明:敏感度场是拓扑预测的信息论最优条件信号。然而,精确计算伴随敏感度在实际中可能昂贵或不可行;我们发现某些物理场可通过单调变换近似敏感度。为此,我们引入【伪敏感度】来刻画哪些场能促进泛化,哪些信息贫乏。实验表明,敏感度条件化的伯努利流匹配生成器有效验证了该理论:以敏感度为条件时达到当前最佳的OOD性能,而与敏感度越远的物理场则退化至仅用参数条件。结果在结构拓扑优化基准及新提出的CFD-TO数据集(含多出口配置等边界条件变化)上均成立。代码与数据集见https://tum-pbs.github.io/topotransformer/。
原文摘要 · Abstract (English)
Surrogate models for topology optimization (TO) exhibit highly variable out-of-distribution (OOD) generalization under distribution shifts such as changing loads or boundary conditions, yet the source of this variability remains unclear. We hypothesize that OOD performance is governed by how much information the conditioning signal preserves about the adjoint sensitivity (reduced gradient) that drives classical TO. Modeling the TO pipeline as a causal Markov chain, the Data Processing Inequality establishes that, under this abstraction, the sensitivity field is an information-theoretically optimal conditioning signal for topology prediction. However, computing exact adjoint sensitivities can be expensive or unavailable in practice; we observe that certain physical fields can approximate sensitivities through monotone transformations. To formalize this, we introduce \textbf{pseudo-sensitivities} to characterize which fields enable generalization versus those that are information-poor. We then show that a sensitivity-conditioned Bernoulli flow-matching generator empirically confirms these predictions: conditioning on sensitivities yields state-of-the-art OOD performance, while increasingly distant physical fields degrade toward raw parameter conditioning. Results hold across structural TO benchmarks under load shifts and our new CFD-TO dataset under boundary-condition shifts such as multi-outlet configurations. Code and datasets are available at https://tum-pbs.github.io/topotransformer/ .
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