mlsanityData to 14 Oct 2026

Neural topology optimization: the good, the bad, and the ugly

arXiv 2407.13954 ↗First posted 19 Jul 2024cs.LG cs.NA math.NAcited by 10

Not on the map. Why?

Abstract (arXiv)

Neural networks (NNs) hold great promise for advancing inverse design via topology optimization (TO), yet misconceptions about their application persist. This article focuses on neural topology optimization (neural TO), which leverages NNs to reparameterize the decision space and reshape the optimization landscape. While the method is still in its infancy, our analysis tools reveal critical insights into the NNs' impact on the optimization process. We demonstrate that the choice of NN architecture significantly influences the objective landscape and the optimizer's path to an optimum. Notably, NNs introduce non-convexities even in otherwise convex landscapes, potentially delaying convergence in convex problems but enhancing exploration for non-convex problems. This analysis lays the groundwork for future advancements by highlighting: 1) the potential of neural TO for non-convex problems and dedicated GPU hardware (the "good"), 2) the limitations in smooth landscapes (the "bad"), and 3) the complex challenge of selecting optimal NN architectures and hyperparameters for superior performance (the "ugly").

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Builds on 27 of its 98 references that are in the map. First posted on arXiv 19 Jul 2024.

Builds on

27 of 98 references.

References · 27

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15 more
  1. 2020Descending through a Crowded Valley - Benchmarking Deep Learning Optimizerscited by 119
  2. 2021Seeing Implicit Neural Representations as Fourier Seriescited by 50
  3. 2019Neural reparameterization improves structural optimizationcited by 44
  4. 2021NTopo: Mesh-free Topology Optimization using Implicit Neural Representationscited by 41
  5. 2017Neural networks for topology optimizationcited by 39
  6. 2021Physics and Equality Constrained Artificial Neural Networks: Application to Forward and Inverse Problems with Multi-fidelity Data Fusioncited by 38
  7. 2022On the use of Artificial Neural Networks in Topology Optimisationcited by 36
  8. 20183D Topology Optimization using Convolutional Neural Networkscited by 29
  9. 2023Distributed Constrained Combinatorial Optimization leveraging Hypergraph Neural Networkscited by 13
  10. 2024Geometry-Informed Neural Networkscited by 12
  11. 2020Computing multiple solutions of topology optimization problemscited by 7
  12. 2014Topology optimization based on moving deformable components: A new computational frameworkcited by 6
  13. 2020An AI-Assisted Design Method for Topology Optimization Without Pre-Optimized Training Datacited by 3
  14. 2021DNN-Based Topology Optimisation: Spatial Invariance and Neural Tangent Kernelcited by 2
  15. 2024Pentagonal Photonic Crystal Mirrors: Scalable Lightsails with Enhanced Acceleration via Neural Topology Optimizationcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 3; 2026: 6.

10 papers.

  1. 2024Neural Networks for Generating Better Local Optima in Topology Optimizationcited by 4
  2. 2025Compliance Minimization via Physics-Informed Gaussian Processescited by 2
  3. 2026Multi-material Multi-physics Topology Optimization with Physics-informed Gaussian Process Priorscited by 2
  4. 2025Diverse Topology Optimization using Modulated Neural Fieldscited by 1
  5. 2026Adversarial Agents on Topology Optimization: Understanding the Fragility and Robustness of Deep Learning-based and Physics-Based Design Models under Adversarial Perturbationcited by 1
  6. 2025Physics-guided denoiser network for enhanced additive manufacturing data qualitycited by 0
  7. 2026Gauss-Newton Natural Gradient Descent for Shape Learningcited by 0
  8. 2026Neural parametric representations for thin-shell shape optimisationcited by 0
  9. 2026Bilevel Optimization of Topology and Hyperparameters (BOTH)cited by 0
  10. 2026How the Classical Baseline Shapes Machine-Learning Speed Claims in Topology Optimizationcited by 0