cs.LGAug 23, 2026

Adversarial Agents on Topology Optimization: Understanding the Fragility and Robustness of Deep Learning-based and Physics-Based Design Models under Adversarial Perturbation

Authors: Hoang Anh Nguyen, Yuan Hong, Hongyi Xu

Organizations: School of Mechanical, Aerospace, and Manufacturing Engineering, University of Connecticut, Storrs, CT 06269 · School of Computing, University of Connecticut, Storrs, CT 06269

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Abstract

Topology optimization, using both physic-based approaches and deep learning surrogates, serves as a cornerstone for generative design agents in cyber-manufacturing systems. While deep learning surrogates have gained widespread adoption due to their speed in online design generation, this work demonstrates their vulnerability under input perturbations. In this work, we present a mechanics-grounded reliability evaluation framework that formulates an adversarial agent targeting the generative design models. We investigate a strictly non-intrusive threat model where bounded perturbations are introduced exclusively to the initial-density channel, while physical boundary conditions, compliance-gradient channels, network architectures, and solver routines remain intact. Evaluating surrogate models across U-Net, convolutional, and generative architectures with varying physics-gradient conditioning depths demonstrates that bounded initialization noise can cause catastrophic mechanical failure, increasing compliance by multiple orders of magnitude through severed load paths and disconnected supports. Furthermore, we discover that incorporating richer physics-gradient conditioning in the deep learning surrogates does not guarantee monotonic robustness across surrogate families. Finally, physics-in-the-loop recovery demonstrates that initializing the classical SIMP optimizer with perturbed topologies mitigates design performance degradation, having a high probability of restoring compliance to near-baseline levels across tested instances. These findings demonstrate that learned surrogates should serve as physics-verified initializers instead of replacing physics-based solvers entirely in a resilient cyber-manufacturing system. Moreover, the proposed adversarial agent provides a foundation for future training generative design agents robust against noise and targeted perturbations.

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Topology optimization finds material layouts that meet performance and manufacturing constraints across engineering systems.

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Shengyu Yan, Jasmin Jelovica

Department of Mechanical Engineering, The University of British Columbia, 6250 Applied Science Ln, Vancouver, V6T 1Z4, Canada · Department of Civil Engineering, The University of British Columbia, 6250 Applied Science Ln, Vancouver, V6T 1Z4, Canada

Neural Surrogate ModelingTopology OptimizationSurrogate ModelingFourier Neural OperatorSurrogate-Assisted Optimization
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Deep generative models offer a promising paradigm for topology optimization, enabling rapid design exploration. However, these approaches lack intrinsic physics guidance, often leading to poor generalizability across unseen boundary conditions and the formation of floating material artifacts. To address these limitations, we propose Hierarchical Physics-Guided Diffusion (HPG-Diff), a novel diffusion framework that enforces physics consistency through two synergistic mechanisms. First, we introduce a hierarchical physics-guided strategy that aligns different precomputed physics features with the denoising process, guiding material distribution toward optimal load paths to enhance generalizability. Second, we propose a floating material suppression loss as a differentiable connectivity constraint inspired by thermal conduction to improve topological connectivity. By simulating a virtual heat propagation process from load positions, this mechanism explicitly penalizes floating material during training. Quantitative evaluations demonstrate that HPG-Diff achieves average compliance errors of 0.87% (in-distribution) and 5.29% (out-of-distribution), while reducing floating material ratios to 2.90% and 2.44%, respectively. Furthermore, case studies on a 3:1 rectangular domain, including cantilever and bridge benchmarks, provide preliminary evidence that lightweight LoRA fine-tuning with a small dataset can support the adaptation of HPG-Diff to rectangular non-square domains.

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