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

arXiv: https://arxiv.org/abs/2608.22606 · HTML: https://mlsanity.com/paper/2608.22606/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 23 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain](https://mlsanity.com/paper/2003.04685/) (2020)
- [Deep learning for determining a near-optimal topological design without any iteration](https://mlsanity.com/paper/1801.05463/) (2018)
- [Neural networks for topology optimization](https://mlsanity.com/paper/1709.09578/) (2017)
- [On the use of Artificial Neural Networks in Topology Optimisation](https://mlsanity.com/paper/2208.02563/) (2022)
- [A Novel Topology Optimization Approach using Conditional Deep Learning](https://mlsanity.com/paper/1901.04859/) (2019)
- [Neural topology optimization: the good, the bad, and the ugly](https://mlsanity.com/paper/2407.13954/) (2024)
- [Latent Diffusion Models for Structural Component Design](https://mlsanity.com/paper/2309.11601/) (2023)
- [On the Generalization in Topology Optimization via Sensitivity-Conditioned Bernoulli Flow Matching](https://mlsanity.com/paper/2606.02179/) (2026)
- [A surrogate model for topology optimisation of elastic structures via parametric autoencoders](https://mlsanity.com/paper/2507.22539/) (2025)
- [An Uncertainty-aware Deep Learning Framework-based Robust Design Optimization of Metamaterial Units](https://mlsanity.com/paper/2407.20251/) (2024)

## Built on by (most cited first, 1 of 1)

- [How the Classical Baseline Shapes Machine-Learning Speed Claims in Topology Optimization](https://mlsanity.com/paper/2610.16051/) (2026)

## Abstract (arXiv)

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.