mlsanityData to 14 Oct 2026

Topology Optimization via Machine Learning and Deep Learning: A Review

arXiv 2210.10782 ↗First posted 19 Oct 2022cs.LGcited by 23

Not on the map. Why?

Abstract (arXiv)

Topology optimization (TO) is a method of deriving an optimal design that satisfies a given load and boundary conditions within a design domain. This method enables effective design without initial design, but has been limited in use due to high computational costs. At the same time, machine learning (ML) methodology including deep learning has made great progress in the 21st century, and accordingly, many studies have been conducted to enable effective and rapid optimization by applying ML to TO. Therefore, this study reviews and analyzes previous research on ML-based TO (MLTO). Two different perspectives of MLTO are used to review studies: (1) TO and (2) ML perspectives. The TO perspective addresses "why" to use ML for TO, while the ML perspective addresses "how" to apply ML to TO. In addition, the limitations of current MLTO research and future research directions are examined.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). Builds on 35 of its 175 references that are in the map. First posted on arXiv 19 Oct 2022.

Builds on

35 of 175 references.

References · 35

  1. 2017Proximal Policy Optimization Algorithmscited by 15,215
  2. 2013Auto-Encoding Variational Bayescited by 4,053
  3. 2013Playing Atari with Deep Reinforcement Learningcited by 3,274
  4. 2015Trust Region Policy Optimizationcited by 2,580
  5. 2016Asynchronous Methods for Deep Reinforcement Learningcited by 2,258
  6. 2014Conditional Generative Adversarial Netscited by 2,162
  7. 2015Deep Reinforcement Learning with Double Q-learningcited by 1,745
  8. 2015A Neural Algorithm of Artistic Stylecited by 483
  9. 2016Energy-based Generative Adversarial Networkcited by 119
  10. 2019An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applicationscited by 118
  11. 2020TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domaincited by 65
  12. 2020Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systemscited by 52
23 more
  1. 2019Neural reparameterization improves structural optimizationcited by 44
  2. 2021NTopo: Mesh-free Topology Optimization using Implicit Neural Representationscited by 41
  3. 2018Deep learning for determining a near-optimal topological design without any iterationcited by 40
  4. 2017Neural networks for topology optimizationcited by 39
  5. 2019Global optimization of dielectric metasurfaces using a physics-driven neural networkcited by 30
  6. 20183D Topology Optimization using Convolutional Neural Networkscited by 29
  7. 2020Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropycited by 23
  8. 2020Fit2Form: 3D Generative Model for Robot Gripper Form Designcited by 21
  9. 2020Generative Design by Reinforcement Learning: Enhancing the Diversity of Topology Optimization Designscited by 19
  10. 2019A Novel Topology Optimization Approach using Conditional Deep Learningcited by 18
  11. 2019A deep Convolutional Neural Network for topology optimization with strong generalization abilitycited by 17
  12. 2021A Deep Collocation Method for the Bending Analysis of Kirchhoff Platecited by 13
  13. 2020Deep Autoencoder based Energy Method for the Bending, Vibration, and Buckling Analysis of Kirchhoff Platescited by 12
  14. 2021Length Scale Control in Topology Optimization using Fourier Enhanced Neural Networkscited by 11
  15. 2020Data-driven topology design using a deep generative modelcited by 6
  16. 2018A novel topology design approach using an integrated deep learning network architecturecited by 5
  17. 2019A New CGAN Technique for Constrained Topology Design Optimizationcited by 5
  18. 2021Topology Optimization Methods for 3D Structural Problems: A Comparative Studycited by 5
  19. 2019Convolutional Neural Network-based Topology Optimization (CNN-TO) By Estimating Sensitivity of Compliance from Material Distributioncited by 4
  20. 2019Progressive-Growing of Generative Adversarial Networks for Metasurface Optimizationcited by 2
  21. 2020Shape related constraints aware generation of Mechanical Designs through Deep Convolutional GANcited by 2
  22. 2020Scalable Deep-Learning-Accelerated Topology Optimization for Additively Manufactured Materialscited by 2
  23. 2020Successive Training of a Generative Adversarial Network for the Design of an Optical Cloakcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 4; 2024: 6; 2025: 5; 2026: 8.

23 papers.

Sort:

By area:

  1. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  2. 2024Geometry-Informed Neural Networkscited by 12
  3. 2023Constraining Generative Models for Engineering Design with Negative Datacited by 11
  4. 2025BikeBench: A Bicycle Design Benchmark for Generative Models with Objectives and Constraintscited by 5
  5. 2023Dynamically configured physics-informed neural network in topology optimization applicationscited by 3
  6. 2024Consistent machine learning for topology optimization with microstructure-dependent neural network material modelscited by 3
  7. 2025A surrogate model for topology optimisation of elastic structures via parametric autoencoderscited by 3
  8. 2025Optimize Any Topology: A Foundation Model for Shape- and Resolution-Free Structural Topology Optimizationcited by 3
  9. 2024Gradient-free neural topology optimization: Towards effective fracture-resistant designscited by 2
  10. 2025Three-dimensional Deep Shape Optimization with a Limited Datasetcited by 2
  11. 2025Compliance Minimization via Physics-Informed Gaussian Processescited by 2
  12. 2024Deep Generative Model-based Synthesis of Four-bar Linkage Mechanisms with Target Conditionscited by 1
11 more
  1. 2026Large Language Models as Optimization Controllers: Adaptive Continuation for SIMP Topology Optimizationcited by 1
  2. 2026KATOsuper: Surrogate-accelerated neural topology optimization with sensitivity-consistent Fourier neural operatorscited by 1
  3. 2023Data-driven intelligent computational design for products: Method, techniques, and applicationscited by 0
  4. 2024Structural Design Through Reinforcement Learningcited by 0
  5. 2024Deep Reinforcement Learning for the Design of Metamaterial Mechanisms with Functional Compliance Controlcited by 0
  6. 2026AutoSiMP: Autonomous Topology Optimization from Natural Language via LLM-Driven Problem Configuration and Adaptive Solver Controlcited by 0
  7. 2026Parametrizing Convex Sets Using Sublinear Neural Networkscited by 0
  8. 2026A Multi-Agent System for Motor Design Optimization via an FEA-AI Hybrid Approachcited by 0
  9. 2026TopoMamba: A Load-Support Relation-Guided Multi-Directional State-Space Model for Topology Optimizationcited by 0
  10. 2026Neural topology optimization of ship structures under propulsion machinery vibrationscited by 0
  11. 2026How the Classical Baseline Shapes Machine-Learning Speed Claims in Topology Optimizationcited by 0