mlsanityData to 7 Oct 2026

Geometry-Informed Neural Networks

arXiv 2402.14009 ↗First posted 21 Feb 2024cs.LG cs.CVcited by 12

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Abstract (arXiv)

Geometry is a ubiquitous tool in computer graphics, design, and engineering. However, the lack of large shape datasets limits the application of state-of-the-art supervised learning methods and motivates the exploration of alternative learning strategies. To this end, we introduce geometry-informed neural networks (GINNs) -- a framework for training shape-generative neural fields without data by leveraging user-specified design requirements in the form of objectives and constraints. By adding diversity as an explicit constraint, GINNs avoid mode-collapse and can generate multiple diverse solutions, often required in geometry tasks. Experimentally, we apply GINNs to several problems spanning physics, geometry, and engineering design, showing control over geometrical and topological properties, such as surface smoothness or the number of holes. These results demonstrate the potential of training shape-generative models without data, paving the way for new generative design approaches without large datasets.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 67 of its 113 references that are in the map. First posted on arXiv 21 Feb 2024.

Builds on

67 of 113 references.

References · 67

  1. 2017Attention Is All You Needcited by 59,932
  2. 2020Language Models are Few-Shot Learnerscited by 32,199
  3. 2020Denoising Diffusion Probabilistic Modelscited by 20,851
  4. 2019DeepSDF: Learning Continuous Signed Distance Functions for Shape Representationcited by 2,682
  5. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,214
  6. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,170
  7. 2015Variational Inference with Normalizing Flowscited by 2,161
  8. 2018Occupancy Networks: Learning 3D Reconstruction in Function Spacecited by 2,037
  9. 2021Alias-Free Generative Adversarial Networkscited by 1,181
  10. 2016Group Equivariant Convolutional Networkscited by 1,154
  11. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  12. 2018Learning Implicit Fields for Generative Shape Modelingcited by 1,060
38 more
  1. 2016HyperNetworkscited by 1,003
  2. 2020Implicit Geometric Regularization for Learning Shapescited by 707
  3. 2019Hamiltonian Neural Networkscited by 702
  4. 2020When and why PINNs fail to train: A neural tangent kernel perspectivecited by 629
  5. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 612
  6. 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 600
  7. 2021Neural Fields in Visual Computing and Beyondcited by 539
  8. 2019SAL: Sign Agnostic Learning of Shapes from Raw Datacited by 389
  9. 2020Lagrangian Neural Networkscited by 388
  10. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 296
  11. 2020Neural Unsigned Distance Fields for Implicit Function Learningcited by 265
  12. 2020Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanismcited by 231
  13. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 223
  14. 2023WIRE: Wavelet Implicit Neural Representationscited by 220
  15. 2019Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systemscited by 203
  16. 2019Topology-Preserving Deep Image Segmentationcited by 198
  17. 2016Theory-guided Data Science: A New Paradigm for Scientific Discovery from Datacited by 169
  18. 2021Modulated Periodic Activations for Generalizable Local Functional Representationscited by 140
  19. 2019A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homologycited by 134
  20. 2016Mode Regularized Generative Adversarial Networkscited by 123
  21. 2020SALD: Sign Agnostic Learning with Derivativescited by 115
  22. 2024Challenges in Training PINNs: A Loss Landscape Perspectivecited by 109
  23. 2021Deep Generative Models in Engineering Design: A Reviewcited by 103
  24. 2022Learning Smooth Neural Functions via Lipschitz Regularizationcited by 86
  25. 2019A Topology Layer for Machine Learningcited by 79
  26. 2021DiGS : Divergence guided shape implicit neural representation for unoriented point cloudscited by 76
  27. 2020Lagrangian Duality for Constrained Deep Learningcited by 72
  28. 2021Incorporating Domain Knowledge into Deep Neural Networkscited by 56
  29. 2021Point-set Distances for Learning Representations of 3D Point Cloudscited by 48
  30. 2021NTopo: Mesh-free Topology Optimization using Implicit Neural Representationscited by 41
  31. 2020Iso-Points: Optimizing Neural Implicit Surfaces with Hybrid Representationscited by 39
  32. 2023Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignmentcited by 39
  33. 2022Enhanced Physics-Informed Neural Networks with Augmented Lagrangian Relaxation Method (AL-PINNs)cited by 35
  34. 2021PcDGAN: A Continuous Conditional Diverse Generative Adversarial Network For Inverse Designcited by 30
  35. 2023An operator preconditioning perspective on training in physics-informed machine learningcited by 27
  36. 2022Exploring Differential Geometry in Neural Implicitscited by 26
  37. 2020Cubical Ripser: Software for computing persistent homology of image and volume datacited by 23
  38. 2022Topology Optimization via Machine Learning and Deep Learning: A Reviewcited by 22

50 most cited of 67 All 67 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 6; 2026: 4.

12 papers.

  1. 2025Scalable Discrete Diffusion Samplers: Combinatorial Optimization and Statistical Physicscited by 28
  2. 2024Neural topology optimization: the good, the bad, and the uglycited by 9
  3. 2024STITCH: Surface reconstrucTion using Implicit neural representations with Topology Constraints and persistent Homologycited by 4
  4. 2025Neural Discovery in Mathematics: Do Machines Dream of Colored Planes?cited by 4
  5. 2025Optimality-Informed Neural Networks for Solving Parametric Optimization Problemscited by 1
  6. 2025Diverse Topology Optimization using Modulated Neural Fieldscited by 0
  7. 2025Minimizing Structural Vibrations via Guided Flow Matching Design Optimizationcited by 0
  8. 2025Intrinsic-Metric Physics-Informed Neural Networks (IM-PINN) for Reaction-Diffusion Dynamics on Complex Riemannian Manifoldscited by 0
  9. 2026Gauss-Newton Natural Gradient Descent for Shape Learningcited by 0
  10. 2026GIBLy: Improving 3D Semantic Segmentation through an Architecture-Agnostic Lightweight Geometric Inductive Bias Layercited by 0
  11. 2026Neural Representation of Minimal Surfacescited by 0
  12. 2026Fourier-Latent Diffusion for Constrained Generation of Triply Periodic Minimal Surfacescited by 0