# Topology Optimization via Machine Learning and Deep Learning: A Review

arXiv: https://arxiv.org/abs/2210.10782 · HTML: https://mlsanity.com/paper/2210.10782/

## 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 (most cited first, 30 of 35)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Deep Reinforcement Learning with Double Q-learning](https://mlsanity.com/paper/1509.06461/) (2015)
- [A Neural Algorithm of Artistic Style](https://mlsanity.com/paper/1508.06576/) (2015)
- [Energy-based Generative Adversarial Network](https://mlsanity.com/paper/1609.03126/) (2016)
- [An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications](https://mlsanity.com/paper/1908.10407/) (2019)
- [TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain](https://mlsanity.com/paper/2003.04685/) (2020)
- [Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems](https://mlsanity.com/paper/2006.15274/) (2020)
- [Neural reparameterization improves structural optimization](https://mlsanity.com/paper/1909.04240/) (2019)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [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)
- [Global optimization of dielectric metasurfaces using a physics-driven neural network](https://mlsanity.com/paper/1906.04157/) (2019)
- [3D Topology Optimization using Convolutional Neural Networks](https://mlsanity.com/paper/1808.07440/) (2018)
- [Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy](https://mlsanity.com/paper/2012.15744/) (2020)
- [Fit2Form: 3D Generative Model for Robot Gripper Form Design](https://mlsanity.com/paper/2011.06498/) (2020)
- [Generative Design by Reinforcement Learning: Enhancing the Diversity of Topology Optimization Designs](https://mlsanity.com/paper/2008.07119/) (2020)
- [A Novel Topology Optimization Approach using Conditional Deep Learning](https://mlsanity.com/paper/1901.04859/) (2019)
- [A deep Convolutional Neural Network for topology optimization with strong generalization ability](https://mlsanity.com/paper/1901.07761/) (2019)
- [A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate](https://mlsanity.com/paper/2102.02617/) (2021)
- [Deep Autoencoder based Energy Method for the Bending, Vibration, and Buckling Analysis of Kirchhoff Plates](https://mlsanity.com/paper/2010.05698/) (2020)
- [Length Scale Control in Topology Optimization using Fourier Enhanced Neural Networks](https://mlsanity.com/paper/2109.01861/) (2021)
- [Data-driven topology design using a deep generative model](https://mlsanity.com/paper/2006.04559/) (2020)
- [A novel topology design approach using an integrated deep learning network architecture](https://mlsanity.com/paper/1808.02334/) (2018)
- [A New CGAN Technique for Constrained Topology Design Optimization](https://mlsanity.com/paper/1901.07675/) (2019)
- [Topology Optimization Methods for 3D Structural Problems: A Comparative Study](https://mlsanity.com/paper/2108.03146/) (2021)

## Built on by (most cited first, 23 of 23)

- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [Geometry-Informed Neural Networks](https://mlsanity.com/paper/2402.14009/) (2024)
- [Constraining Generative Models for Engineering Design with Negative Data](https://mlsanity.com/paper/2306.15166/) (2023)
- [BikeBench: A Bicycle Design Benchmark for Generative Models with Objectives and Constraints](https://mlsanity.com/paper/2508.00830/) (2025)
- [Dynamically configured physics-informed neural network in topology optimization applications](https://mlsanity.com/paper/2312.06993/) (2023)
- [Consistent machine learning for topology optimization with microstructure-dependent neural network material models](https://mlsanity.com/paper/2408.13843/) (2024)
- [A surrogate model for topology optimisation of elastic structures via parametric autoencoders](https://mlsanity.com/paper/2507.22539/) (2025)
- [Optimize Any Topology: A Foundation Model for Shape- and Resolution-Free Structural Topology Optimization](https://mlsanity.com/paper/2510.23667/) (2025)
- [Gradient-free neural topology optimization: Towards effective fracture-resistant designs](https://mlsanity.com/paper/2403.04937/) (2024)
- [Three-dimensional Deep Shape Optimization with a Limited Dataset](https://mlsanity.com/paper/2506.12326/) (2025)
- [Compliance Minimization via Physics-Informed Gaussian Processes](https://mlsanity.com/paper/2507.09968/) (2025)
- [Deep Generative Model-based Synthesis of Four-bar Linkage Mechanisms with Target Conditions](https://mlsanity.com/paper/2402.14882/) (2024)
- [Large Language Models as Optimization Controllers: Adaptive Continuation for SIMP Topology Optimization](https://mlsanity.com/paper/2603.25099/) (2026)
- [KATOsuper: Surrogate-accelerated neural topology optimization with sensitivity-consistent Fourier neural operators](https://mlsanity.com/paper/2609.27216/) (2026)
- [Data-driven intelligent computational design for products: Method, techniques, and applications](https://mlsanity.com/paper/2301.12382/) (2023)
- [Structural Design Through Reinforcement Learning](https://mlsanity.com/paper/2407.07288/) (2024)
- [Deep Reinforcement Learning for the Design of Metamaterial Mechanisms with Functional Compliance Control](https://mlsanity.com/paper/2408.04376/) (2024)
- [AutoSiMP: Autonomous Topology Optimization from Natural Language via LLM-Driven Problem Configuration and Adaptive Solver Control](https://mlsanity.com/paper/2603.27000/) (2026)
- [Parametrizing Convex Sets Using Sublinear Neural Networks](https://mlsanity.com/paper/2605.03520/) (2026)
- [A Multi-Agent System for Motor Design Optimization via an FEA-AI Hybrid Approach](https://mlsanity.com/paper/2606.09037/) (2026)
- [TopoMamba: A Load-Support Relation-Guided Multi-Directional State-Space Model for Topology Optimization](https://mlsanity.com/paper/2609.33688/) (2026)
- [Neural topology optimization of ship structures under propulsion machinery vibrations](https://mlsanity.com/paper/2609.38089/) (2026)
- [How the Classical Baseline Shapes Machine-Learning Speed Claims in Topology Optimization](https://mlsanity.com/paper/2610.16051/) (2026)

## 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.