On the Generalization in Topology Optimization via Sensitivity-Conditioned Bernoulli Flow Matching
2026-06-01 • Machine Learning
Machine LearningArtificial IntelligenceComputational Engineering, Finance, and Science
AI summaryⓘ
The authors studied why surrogate models for topology optimization (TO) struggle to perform well when conditions like loads or boundaries change. They proposed that how much useful information the model keeps about a key factor called the adjoint sensitivity (which guides the optimization) affects how well it generalizes out-of-distribution. They introduced the idea of "pseudo-sensitivities" to identify which physical signals approximate this sensitivity well enough. Their experiments showed that models conditioned on true sensitivities perform best, while those using less related information do worse. This was tested on several structural and fluid dynamics TO problems with varying conditions.
topology optimizationsurrogate modelsout-of-distribution generalizationadjoint sensitivityData Processing Inequalitypseudo-sensitivitiesBernoulli flow-matchingcausal Markov chainload shiftsboundary conditions
Authors
Mohammad Rashed, Duarte F. Valoroso Madeira, Babak Gholami, Caglar Guerbuez, Yunjia Yang, Nils Thuerey
Abstract
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/ .