Title: Enhancing Generalization in Topology Optimization Through Sensitivity-Conditioned Bernoulli Flow Matching

Abstract:

Surrogate models employed in topology optimization (TO) frequently demonstrate inconsistent out-of-distribution (OOD) generalization capabilities when subjected to distributional shifts, such as variations in loads or boundary conditions. Despite this, the underlying causes of such variability remain poorly understood. This study posits that OOD performance is fundamentally dictated by the extent to which the conditioning signal retains information regarding the adjoint sensitivity—the reduced gradient that underpins classical TO. By framing the TO pipeline as a causal Markov chain, we apply the Data Processing Inequality to demonstrate that, within this theoretical framework, the sensitivity field serves as the information-theoretically superior conditioning signal for predicting topology.

Although calculating exact adjoint sensitivities is often computationally prohibitive or entirely inaccessible in practical scenarios, we identify that specific physical fields can approximate these sensitivities via monotone transformations. To rigorously define which fields facilitate generalization and which are information-poor, we introduce the concept of pseudo-sensitivities. Empirical validation using a sensitivity-conditioned Bernoulli flow-matching generator supports these theoretical predictions: conditioning on sensitivities achieves state-of-the-art OOD performance, whereas reliance on physical fields increasingly distant from true sensitivities results in performance degradation comparable to raw parameter conditioning. These findings are validated across structural TO benchmarks involving load shifts and a novel CFD-TO dataset featuring boundary-condition shifts, such as multi-outlet configurations. Code and datasets are accessible at https://tum-pbs.github.io/topotransformer/ .

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC