Topology Optimization

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Topology optimization determines where material should be placed or removed to improve goals such as stiffness, vibration control, heat transfer, or actuator motion while respecting constraints. Established approaches include density-based SIMP, level-set methods, and evolutionary methods such as BESO, typically paired with finite-element analysis and sensitivity-based optimization. Newer work uses neural surrogates, graph models, and generative methods to speed up or automate design, and extends optimization to multiple materials, coupled physics, and robotic co-design. A central challenge is achieving speed and generalization without sacrificing physical accuracy, robustness, manufacturability, or fair comparison with well-tuned classical solvers.

Latest papers

34 papers6 papers in the last four weeks, up 20% on the four weeks before. 0.0% of all new papers.

Scalable Stress-Constrained Topology Optimization: A Super-resolution and Simultaneous Approach Based on Machine Learning
Oct 20, 2026Xiangyu Sun, Shirin Hosseinmardi, Ramin BostanabadTopology Optimization
Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA · Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA · Department of Civil and Environmental Engineering, University of California, Irvine, CA, USA
Concurrent two-scale topology optimization of printable bone scaffolds via rectified-flow generation and exact latent-space refinement
Oct 18, 2026Reza T Batley, Sourav SahaTopology Optimization Latent Space Optimization
Kevin T Crofton Department of Aerospace and Ocean Engineering, Virginia Tech, 1600 Innovation Drive, Blacksburg, 24060, VA, United States
How the Classical Baseline Shapes Machine-Learning Speed Claims in Topology Optimization
Oct 12, 2026Shaoliang Yang, Jun WangTopology Optimization
Santa Clara University Santa Clara, CA 95053, USA
Toward Maximizing Algebraic Connectivity via Density-Dependent Backbone Construction and Reinforcement Learning Completion
Oct 8, 2026Zeru Zhu, Marco Gamarra, Ji LiuGraph Construction Topology Optimization
Department of Applied Mathematics and Statistics at Stony Brook University · Air Force Research Laboratory · Department of Electrical and Computer Engineering at Stony Brook University
TO-mdiSPAs: Topology Optimization of multi-directional Soft Pneumatic Actuators
Sep 30, 2026Swagatam Islam Sarkar, Prabhat KumarTopology Optimization Soft Pneumatic Actuators
Department of Mechanical and Aerospace Engineering Indian Institute of Technology Hyderabad Telangana-502284, India
Neural topology optimization of ship structures under propulsion machinery vibrations
Sep 29, 2026Shengyu Yan, Muhammad Muztahidul Hakim Zareer, Jasmin JelovicaTopology Optimization
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
TopoMamba: A Load-Support Relation-Guided Multi-Directional State-Space Model for Topology Optimization
Sep 27, 2026Bin Lou, Yuxuan Cheng, Huaizhi Zong +2Neural Surrogate Modeling Topology Optimization
State Key Laboratory of Fluid Power and Mechatronic Systems Zhejiang University Hangzhou
KATOsuper: Surrogate-accelerated neural topology optimization with sensitivity-consistent Fourier neural operators
Sep 23, 2026Shengyu Yan, Jasmin JelovicaNeural Surrogate Modeling Topology Optimization
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
Bilevel Optimization of Topology and Hyperparameters (BOTH)
Sep 18, 2026Suryanarayanan Manoj Sanu, Miguel Anibal Bessa, Alejandro Marcos AragónHypergradient Optimization Topology Optimization
Faculty of Mechanical Engineering Delft university of technology Delft The Netherlands · School of engineering Brown University Providence United States of America
HGTO: A Unified Graph-Based Physics-Informed Formulation for Structural Topology Optimization
Sep 14, 2026Kangzheng Liu, Uday Kumar Punna, Leixin MaTopology Optimization Structural Mechanics
School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, 85287, AZ, USA
Zero-shot rib design: merging training-free generative prior with topology optimization
Sep 9, 2026Yongmin Kwon, Namwoo KangTopology Optimization Structural Mechanics
Cho Chun Shik Graduate School of Mobility, Korea Advanced Institute of Science and Technology, 193 Munji-ro, Yuseong-gu, Daejeon, 34051, Republic of Korea · AI Research Team, Narnia Labs, 193 Munji-ro, Yuseong-gu, Daejeon, 34051, Republic of Korea
Adversarial Agents on Topology Optimization: Understanding the Fragility and Robustness of Deep Learning-based and Physics-Based Design Models under Adversarial Perturbation
Aug 23, 2026Hoang Anh Nguyen, Yuan Hong, Hongyi XuTopology Optimization Adversarial Robustness
School of Mechanical, Aerospace, and Manufacturing Engineering, University of Connecticut, Storrs, CT 06269 · School of Computing, University of Connecticut, Storrs, CT 06269
On the Importance of Geometric Nonlinearity and Temperature-Dependent Properties in Multi-Material Thermo-Mechanical Topology Optimization
Aug 11, 2026Shirin Hosseinmardi, Xiangyu Sun, Ramin BostanabadTopology Optimization Mechanism Design
Department of Mechanical and Aerospace Engineering, University of California, Irvine · Department of Civil and Environmental Engineering, University of California, Irvine
On the Potential of Graph Neural Networks as Metamodels for Supply Chain Optimization: Dataset, Architectures, and Directions
Jul 18, 2026Tushar Lone, Neha KaranjkarNeural Surrogate Modeling Topology Optimization
School of Mathematics and Computer Science, Indian Institute of Technology Goa, Ponda, Goa, INDIA
Trajectory-Aware Flow Matching for Topology Optimisation
Jul 16, 2026Shusheng Xiao, Jinshuai Bai, Hyogu Jeong +3Topology Optimization Flow Matching
School of Mechanical, Medical and Process Engineering, Queensland University of Technology, Brisbane, 4000, QLD, Australia · Institute of Biomechanics and Medical Engineering, AML, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China · State Key Laboratory of Advanced Environmental Technology, Guangzhou Institute of Geochemistry, Chinese Academy of Sciences, Guangzhou, 510640, China +1
SPECS: Speciated Evolutionary Circuit Synthesis
Jul 15, 2026Yağız Gençer, Stefan Uhlich, Andrea Bonetti +3Topology Optimization Electronic Design Automation
Sony Group Corporation, Switzerland · TU Munich, Germany
Towards end-to-end optimization in multimaterial 3D printing
Jul 14, 2026Xue-Ling Luo, Steven Yang, Jingye Tan +3Neural Surrogate Modeling Topology Optimization
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY, USA · Department of Aerospace & Mechanical Engineering, University of Southern California, Los Angeles, CA, USA · Department of Materials Science and Engineering, Technion - Israel Institute of Technology, Haifa, Israel +1
HPG-Diff: Hierarchical physics-guided diffusion with differentiable connectivity constraints for topology optimization
Jul 8, 2026Jinbo Yang, Mingyue Yuan, Boyuan Zhang +2Topology Optimization Physics-Informed Diffusion Models
School of Mechanical Engineering, Beijing Institute of Technology, Beijing, 100081, China · Computer Science and Engineering, University of New South Wales, Sydney, 2052, Australia · College of Intelligence and Computing, Tianjin University, Tianjin, 300072, China +1
Hardware Design for Table Tennis Robot Capable of Beating Professional Players
Jun 25, 2026Nobuhiko Mukai, Pavel Adodin, Stefan Heusser +6Robot Dynamics Identification Topology Optimization
Sony AI in Tokyo, Japan · Sony AI in Zürich, Switzerland · Sony Global Manufacturing & Operations in Tokyo, Japan
eCNNTO: A Highly Generalizable ConvNet for Accelerating Topology Optimization
Jun 18, 2026Shengbiao Lu, Xiaodong WeiTopology Optimization Deep Learning Optimization
Global college, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, Shanghai, China
TO-SoFiT: Topology Optimization of Hydraulic Soft Fish Tail Design for programmable undulating locomotion
Jun 14, 2026A Padmaprabhan, Amal Shaji, Prabhat KumarTopology Optimization Underwater Robotics
Indian Institute of Technology Hyderabad Telangana, 502285, India
On the Generalization in Topology Optimization via Sensitivity-Conditioned Bernoulli Flow Matching
Jun 1, 2026Mohammad Rashed, Duarte F. Valoroso Madeira, Babak Gholami +3Neural Surrogate Modeling Topology Optimization
School of Computation, Information and Technology, Technical University of Munich, Germany · BMW AG, Munich, Germany · Munich Center for Machine Learning, Munich, Germany. +1
Self-Refining Topology Optimization via an LLM-Based Multi-Agent Framework
May 22, 2026Hyunjee Park, Hayoung ChungTopology Optimization Multi-Agent LLM Systems
Department of Mechanical Engineering, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Ulju-gun, Ulsan, 44919, Republic of Korea
TO-Agents: A Multi-Agent AI Pipeline for Preference-Guided Topology Optimization
May 20, 2026Isabella A. Stewart, Hongrui Chen, Faez AhmedTopology Optimization Multi-Agent System Optimization
Department of Civil and Environmental Engineering Massachusetts Institute of Technology Cambridge, MA, 02139 USA · Department of Mechanical Engineering Massachusetts Institute of Technology Cambridge, MA, 02139 USA
Topology-Optimized Pneumatic Soft Actuator: Design and Experimental Validation
May 19, 2026Sumit Mehta, Konstantinos PouliosTopology Optimization Soft Pneumatic Actuators
Department of Civil and Mechanical Engineering Technical University of Denmark, Denmark
COSMIC: Concurrent Optimization of Structure, Material, and Integrated Control for robotic systems
May 12, 2026Qinsong Guo, Liwei WangTopology Optimization Robot Morphology-Control Co-Design
Dept. of Mechanical Engineering Carnegie Mellon University Pittsburgh, PA 15213
TOPCELL: Topology Optimization of Standard Cell via LLMs
Apr 15, 2026Zhan Song, Yu-Tung Liu, Chen Chen +6Topology Optimization Electronic Design Automation
University of Maryland College Park, USA · NVIDIA Santa Clara, CA, USA · NVIDIA Austin, TX, USA
AutoSiMP: Autonomous Topology Optimization from Natural Language via LLM-Driven Problem Configuration and Adaptive Solver Control
Mar 27, 2026Shaoliang Yang, Jun Wang, Yunsheng WangTopology Optimization Natural Language to Optimization Modeling
Santa Clara University, Santa Clara, CA
Large Language Models as Optimization Controllers: Adaptive Continuation for SIMP Topology Optimization
Mar 26, 2026Shaoliang Yang, Jun Wang, Yunsheng WangTopology Optimization Large Language Model-Guided Optimization
Department of Mechanical Engineering, Santa Clara University, Santa Clara, CA 95053, USA
A Bi-Stage Framework for Automatic Development of Pixel-Based Planar Antenna Structures
Mar 4, 2026Khadijeh Askaripour, Adrian Bekasiewicz, Slawomir KozielTopology Optimization
Faculty of Electronics, Telecommunications and Informatics, Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdansk, Poland · Department of Engineering, Reykjavik University, Menntavegur 1, 102 Reykjavik, Iceland

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Scalable Stress-Constrained Topology Optimization: A Super-resolution and Simultaneous Approach Based on Machine Learning

Xiangyu Sun, Shirin Hosseinmardi, Ramin Bostanabad

Department of Mechanical and Aerospace Engineering, University of California, Irvine, CA, USA · Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA · Department of Civil and Environmental Engineering, University of California, Irvine, CA, USA

Topology Optimization

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Large-scale topology optimization (TO) remains computationally demanding, especially for stress-constrained problems. To address this challenge, we propose the simultaneous neural topology optimization (SNTO) framework where we represent state, adjoint, and design variables with custom neural networks (NNs) whose parameters are jointly optimized within a single optimization loop that leverages continuous adjoint analysis and automatic differentiation. This optimization minimizes a multi-component loss function that combines the design objective, an aggregation of the local stress constraints, and the potential energy functionals. Our NNs have a unique architecture that accelerates convergence while enabling the networks to capture sharp gradients and boundaries which are critical to stress-constrained TO. To achieve scalability to millions of degrees of freedom (DoF), we develop a hardware-aware training scheme in which the design domain is partitioned into subdomains that are distributed across multiple GPUs. To control peak GPU memory usage, we further slice each subdomain into smaller regions whose loss gradients are evaluated sequentially and accumulated to update the NN parameters. Unlike domain decomposition approaches, our partitioning naturally ensures field continuity across the subdomains and does not require the introduction of additional terms into the loss function. For validation, we first evaluate the proposed framework on various 2D stress-constrained benchmarks and compare our results to a conventional finite element-based approach, showing that SNTO produces super-resolution designs with sharper boundaries, smaller gray areas, and lower volume fractions. We then consider large-scale 3D problems with up to eight million collocation points and distribute the training over up to eight GPUs.