mlsanityData to 7 Oct 2026

NTopo: Mesh-free Topology Optimization using Implicit Neural Representations

arXiv 2102.10782 ↗First posted 22 Feb 2021cs.LGcited by 41

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Abstract (arXiv)

Recent advances in implicit neural representations show great promise when it comes to generating numerical solutions to partial differential equations. Compared to conventional alternatives, such representations employ parameterized neural networks to define, in a mesh-free manner, signals that are highly-detailed, continuous, and fully differentiable. In this work, we present a novel machine learning approach for topology optimization -- an important class of inverse problems with high-dimensional parameter spaces and highly nonlinear objective landscapes. To effectively leverage neural representations in the context of mesh-free topology optimization, we use multilayer perceptrons to parameterize both density and displacement fields. Our experiments indicate that our method is highly competitive for minimizing structural compliance objectives, and it enables self-supervised learning of continuous solution spaces for topology optimization problems.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). Builds on 23 of its 67 references that are in the map. First posted on arXiv 22 Feb 2021.

Builds on

23 of 67 references.

References · 23

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  2. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  3. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
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  10. 2020PIFuHD: Multi-Level Pixel-Aligned Implicit Function for High-Resolution 3D Human Digitizationcited by 521
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  12. 2021Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapescited by 426
11 more
  1. 2019DiffTaichi: Differentiable Programming for Physical Simulationcited by 248
  2. 2020Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solverscited by 201
  3. 2020Learning to Control PDEs with Differentiable Physicscited by 131
  4. 2018ChainQueen: A Real-Time Differentiable Physical Simulator for Soft Roboticscited by 98
  5. 2020Physics informed deep learning for computational elastodynamics without labeled datacited by 79
  6. 2020TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domaincited by 65
  7. 2020NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation frameworkcited by 58
  8. 2019Neural reparameterization improves structural optimizationcited by 44
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  11. 2019A deep Convolutional Neural Network for topology optimization with strong generalization abilitycited by 16

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 8; 2023: 8; 2024: 10; 2025: 8; 2026: 6.

41 papers.

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  1. 2021Neural Fields in Visual Computing and Beyondcited by 539
  2. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  3. 2022CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representationscited by 56
  4. 2022Implicit Neural Spatial Representations for Time-dependent PDEscited by 35
  5. 2022Gradient-based Bi-level Optimization for Deep Learning: A Surveycited by 26
  6. 2024Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulationcited by 26
  7. 2023Neural Stress Fields for Reduced-order Elastoplasticity and Fracturecited by 24
  8. 2022Topology Optimization via Machine Learning and Deep Learning: A Reviewcited by 22
  9. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  10. 2022On Quantizing Implicit Neural Representationscited by 20
  11. 2024Geometry-Informed Neural Networkscited by 12
  12. 2024Quaffure: Real-Time Quasi-Static Neural Hair Simulationcited by 10
29 more
  1. 2024Neural topology optimization: the good, the bad, and the uglycited by 9
  2. 2025Explorable INR: An Implicit Neural Representation for Ensemble Simulation Enabling Efficient Spatial and Parameter Explorationcited by 8
  3. 2023Differentiable Visual Computing for Inverse Problems and Machine Learningcited by 7
  4. 2023DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networkscited by 6
  5. 2023NeuralClothSim: Neural Deformation Fields Meet the Thin Shell Theorycited by 6
  6. 2023Neural Metamaterial Networks for Nonlinear Material Designcited by 5
  7. 2024Simultaneous and Meshfree Topology Optimization with Physics-informed Gaussian Processescited by 5
  8. 2022A Generalized Framework for Microstructural Optimization using Neural Networkscited by 3
  9. 2023Topology Optimization using Neural Networks with Conditioning Field Initialization for Improved Efficiencycited by 3
  10. 2024NITO: Neural Implicit Fields for Resolution-free Topology Optimizationcited by 3
  11. 2024Neurally Integrated Finite Elements for Differentiable Elasticity on Evolving Domainscited by 3
  12. 2024Improving Efficiency of Iso-Surface Extraction on Implicit Neural Representations Using Uncertainty Propagationcited by 2
  13. 2025TopoGaussian: Inferring Internal Topology Structures from Visual Cluescited by 2
  14. 2025Compliance Minimization via Physics-Informed Gaussian Processescited by 2
  15. 2023Edge Preserving Implicit Surface Representation of Point Cloudscited by 1
  16. 2024Multi-scale Topology Optimization using Neural Networkscited by 1
  17. 2025Regularized interpolation in 4D neural fields enables optimization of 3D printed geometriescited by 1
  18. 2026GenVoid: Uncertainty-Aware Learning of Subsurface Material Defects with an Experimentally Validated Physics-Informed Generative Modelcited by 1
  19. 2022SELTO: Sample-Efficient Learned Topology Optimizationcited by 0
  20. 2024Machine Learning Optimized Approach for Parameter Selection in MESHFREE Simulationscited by 0
  21. 2025Rigid Body Adversarial Attackscited by 0
  22. 2025Diverse Topology Optimization using Modulated Neural Fieldscited by 0
  23. 2025Censored Sampling for Topology Design: Guiding Diffusion with Human Preferencescited by 0
  24. 2025Heterogeneous Metamaterials Design via Multiscale Neural Implicit Representationcited by 0
  25. 2026Neural parametric representations for thin-shell shape optimisationcited by 0
  26. 2026Differentiable Multiphysics Co-Optimization via Implicit Neural Representations: A Transient Hamburger-Cooking Benchmarkcited by 0
  27. 2026Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospectscited by 0
  28. 2026HoloTetSphere: Unified TetSphere Mesh Reconstruction for Physical Simulationscited by 0
  29. 2026HGTO: A Unified Graph-Based Physics-Informed Formulation for Structural Topology Optimizationcited by 0