On the Generalization in Topology Optimization via Sensitivity-Conditioned Bernoulli Flow Matching

2026-06-01

AI Summary

This work addresses the poor out-of-distribution generalization of existing surrogate models in topology optimization, particularly under varying loads or boundary conditions—a limitation whose root cause remains unclear. By modeling topology optimization as a causal Markov chain, this study offers the first information-theoretic perspective revealing the critical role of adjoint sensitivities in generalization. The authors introduce “pseudo-sensitivity” to quantify the informational efficacy of physical fields and propose a Bernoulli flow matching generative model conditioned on sensitivity. Experiments on structural topology optimization and a newly introduced CFD-TO dataset demonstrate that the method significantly outperforms current approaches under shifts in loading conditions and multi-outlet boundary configurations, achieving state-of-the-art out-of-distribution generalization performance.

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/ .

Problem

• topology optimization
• out-of-distribution generalization
• adjoint sensitivity
• distribution shift
• surrogate models

Innovation

• sensitivity-conditioned
• Bernoulli flow matching
• out-of-distribution generalization
• pseudo-sensitivities
• topology optimization