NTopo: Mesh-free Topology Optimization using Implicit Neural Representations
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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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- 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
- 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
- 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
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- 2021Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapescited by 426
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- 2019DiffTaichi: Differentiable Programming for Physical Simulationcited by 248
- 2020Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solverscited by 201
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- 2020TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domaincited by 65
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Citing papers per year: 2021: 1; 2022: 8; 2023: 8; 2024: 10; 2025: 8; 2026: 6.
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- 2021Neural Fields in Visual Computing and Beyondcited by 539
- 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
- 2022CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representationscited by 56
- 2022Implicit Neural Spatial Representations for Time-dependent PDEscited by 35
- 2022Gradient-based Bi-level Optimization for Deep Learning: A Surveycited by 26
- 2024Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulationcited by 26
- 2023Neural Stress Fields for Reduced-order Elastoplasticity and Fracturecited by 24
- 2022Topology Optimization via Machine Learning and Deep Learning: A Reviewcited by 22
- 2023Deep Learning in Deterministic Computational Mechanicscited by 21
- 2022On Quantizing Implicit Neural Representationscited by 20
- 2024Geometry-Informed Neural Networkscited by 12
- 2024Quaffure: Real-Time Quasi-Static Neural Hair Simulationcited by 10
29 more
- 2024Neural topology optimization: the good, the bad, and the uglycited by 9
- 2025Explorable INR: An Implicit Neural Representation for Ensemble Simulation Enabling Efficient Spatial and Parameter Explorationcited by 8
- 2023Differentiable Visual Computing for Inverse Problems and Machine Learningcited by 7
- 2023DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networkscited by 6
- 2023NeuralClothSim: Neural Deformation Fields Meet the Thin Shell Theorycited by 6
- 2023Neural Metamaterial Networks for Nonlinear Material Designcited by 5
- 2024Simultaneous and Meshfree Topology Optimization with Physics-informed Gaussian Processescited by 5
- 2022A Generalized Framework for Microstructural Optimization using Neural Networkscited by 3
- 2023Topology Optimization using Neural Networks with Conditioning Field Initialization for Improved Efficiencycited by 3
- 2024NITO: Neural Implicit Fields for Resolution-free Topology Optimizationcited by 3
- 2024Neurally Integrated Finite Elements for Differentiable Elasticity on Evolving Domainscited by 3
- 2024Improving Efficiency of Iso-Surface Extraction on Implicit Neural Representations Using Uncertainty Propagationcited by 2
- 2025TopoGaussian: Inferring Internal Topology Structures from Visual Cluescited by 2
- 2025Compliance Minimization via Physics-Informed Gaussian Processescited by 2
- 2023Edge Preserving Implicit Surface Representation of Point Cloudscited by 1
- 2024Multi-scale Topology Optimization using Neural Networkscited by 1
- 2025Regularized interpolation in 4D neural fields enables optimization of 3D printed geometriescited by 1
- 2026GenVoid: Uncertainty-Aware Learning of Subsurface Material Defects with an Experimentally Validated Physics-Informed Generative Modelcited by 1
- 2022SELTO: Sample-Efficient Learned Topology Optimizationcited by 0
- 2024Machine Learning Optimized Approach for Parameter Selection in MESHFREE Simulationscited by 0
- 2025Rigid Body Adversarial Attackscited by 0
- 2025Diverse Topology Optimization using Modulated Neural Fieldscited by 0
- 2025Censored Sampling for Topology Design: Guiding Diffusion with Human Preferencescited by 0
- 2025Heterogeneous Metamaterials Design via Multiscale Neural Implicit Representationcited by 0
- 2026Neural parametric representations for thin-shell shape optimisationcited by 0
- 2026Differentiable Multiphysics Co-Optimization via Implicit Neural Representations: A Transient Hamburger-Cooking Benchmarkcited by 0
- 2026Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospectscited by 0
- 2026HoloTetSphere: Unified TetSphere Mesh Reconstruction for Physical Simulationscited by 0
- 2026HGTO: A Unified Graph-Based Physics-Informed Formulation for Structural Topology Optimizationcited by 0
- 2026GenVoid: Uncertainty-Aware Learning of Subsurface Material Defects with an Experimentally Validated Physics-Informed Generative Model20 Sep 2026
- 2026HGTO: A Unified Graph-Based Physics-Informed Formulation for Structural Topology Optimization14 Sep 2026
- 2026HoloTetSphere: Unified TetSphere Mesh Reconstruction for Physical Simulations9 Jul 2026
- 2026Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects16 May 2026
- 2026Differentiable Multiphysics Co-Optimization via Implicit Neural Representations: A Transient Hamburger-Cooking Benchmark1 May 2026
- 2026Neural parametric representations for thin-shell shape optimisation8 Apr 2026
- 2025Heterogeneous Metamaterials Design via Multiscale Neural Implicit Representation4 Nov 2025
- 2025Censored Sampling for Topology Design: Guiding Diffusion with Human Preferences3 Aug 2025
- 2025Compliance Minimization via Physics-Informed Gaussian Processes14 Jul 2025
- 2025Explorable INR: An Implicit Neural Representation for Ensemble Simulation Enabling Efficient Spatial and Parameter Exploration1 Apr 2025
- 2025TopoGaussian: Inferring Internal Topology Structures from Visual Clues16 Mar 2025
- 2025Diverse Topology Optimization using Modulated Neural Fields17 Feb 2025
29 more
- 2025Rigid Body Adversarial Attacks8 Feb 2025
- 2025Regularized interpolation in 4D neural fields enables optimization of 3D printed geometries3 Feb 2025
- 2024Quaffure: Real-Time Quasi-Static Neural Hair Simulation13 Dec 2024
- 2024Neurally Integrated Finite Elements for Differentiable Elasticity on Evolving Domains12 Oct 2024
- 2024Simultaneous and Meshfree Topology Optimization with Physics-informed Gaussian Processes7 Aug 2024
- 2024Neural topology optimization: the good, the bad, and the ugly19 Jul 2024
- 2024Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulation9 Jun 2024
- 2024Multi-scale Topology Optimization using Neural Networks11 Apr 2024
- 2024Machine Learning Optimized Approach for Parameter Selection in MESHFREE Simulations20 Mar 2024
- 2024Geometry-Informed Neural Networks21 Feb 2024
- 2024Improving Efficiency of Iso-Surface Extraction on Implicit Neural Representations Using Uncertainty Propagation21 Feb 2024
- 2024NITO: Neural Implicit Fields for Resolution-free Topology Optimization7 Feb 2024
- 2023Differentiable Visual Computing for Inverse Problems and Machine Learning21 Nov 2023
- 2023Neural Stress Fields for Reduced-order Elastoplasticity and Fracture26 Oct 2023
- 2023Deep Learning in Deterministic Computational Mechanics27 Sep 2023
- 2023Neural Metamaterial Networks for Nonlinear Material Design15 Sep 2023
- 2023NeuralClothSim: Neural Deformation Fields Meet the Thin Shell Theory24 Aug 2023
- 2023Topology Optimization using Neural Networks with Conditioning Field Initialization for Improved Efficiency17 May 2023
- 2023DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networks6 May 2023
- 2023Edge Preserving Implicit Surface Representation of Point Clouds12 Jan 2023
- 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications15 Nov 2022
- 2022Topology Optimization via Machine Learning and Deep Learning: A Review19 Oct 2022
- 2022Implicit Neural Spatial Representations for Time-dependent PDEs30 Sep 2022
- 2022SELTO: Sample-Efficient Learned Topology Optimization12 Sep 2022
- 2022On Quantizing Implicit Neural Representations1 Sep 2022
- 2022Gradient-based Bi-level Optimization for Deep Learning: A Survey24 Jul 2022
- 2022A Generalized Framework for Microstructural Optimization using Neural Networks13 Jul 2022
- 2022CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations6 Jun 2022
- 2021Neural Fields in Visual Computing and Beyond22 Nov 2021
- 2021Neural Fields in Visual Computing and Beyondcited by 539
- 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
- 2022CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representationscited by 56
- 2022Implicit Neural Spatial Representations for Time-dependent PDEscited by 35
- 2022Gradient-based Bi-level Optimization for Deep Learning: A Surveycited by 26
- 2024Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulationcited by 26
- 2023Neural Stress Fields for Reduced-order Elastoplasticity and Fracturecited by 24
- 2022Topology Optimization via Machine Learning and Deep Learning: A Reviewcited by 22
- 2023Deep Learning in Deterministic Computational Mechanicscited by 21
- 2022On Quantizing Implicit Neural Representationscited by 20
- 2024Geometry-Informed Neural Networkscited by 12
- 2024Quaffure: Real-Time Quasi-Static Neural Hair Simulationcited by 10
12 most cited of 40 All 40 (JSON)
- 2026GenVoid: Uncertainty-Aware Learning of Subsurface Material Defects with an Experimentally Validated Physics-Informed Generative Model20 Sep 2026
- 2026HGTO: A Unified Graph-Based Physics-Informed Formulation for Structural Topology Optimization14 Sep 2026
- 2026HoloTetSphere: Unified TetSphere Mesh Reconstruction for Physical Simulations9 Jul 2026
- 2026Harnessing AI for Inverse Partial Differential Equation Problems: Past, Present, and Prospects16 May 2026
- 2026Differentiable Multiphysics Co-Optimization via Implicit Neural Representations: A Transient Hamburger-Cooking Benchmark1 May 2026
- 2026Neural parametric representations for thin-shell shape optimisation8 Apr 2026
- 2025Heterogeneous Metamaterials Design via Multiscale Neural Implicit Representation4 Nov 2025
- 2025Compliance Minimization via Physics-Informed Gaussian Processes14 Jul 2025
- 2025Explorable INR: An Implicit Neural Representation for Ensemble Simulation Enabling Efficient Spatial and Parameter Exploration1 Apr 2025
- 2025TopoGaussian: Inferring Internal Topology Structures from Visual Clues16 Mar 2025
- 2025Diverse Topology Optimization using Modulated Neural Fields17 Feb 2025
- 2025Rigid Body Adversarial Attacks8 Feb 2025
12 newest of 40 All 40 (JSON)