mlsanityData to 7 Oct 2026

Neural reparameterization improves structural optimization

arXiv 1909.04240 ↗First posted 10 Sep 2019cs.LG cs.NE stat.MLcited by 44

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Abstract (arXiv)

Structural optimization is a popular method for designing objects such as bridge trusses, airplane wings, and optical devices. Unfortunately, the quality of solutions depends heavily on how the problem is parameterized. In this paper, we propose using the implicit bias over functions induced by neural networks to improve the parameterization of structural optimization. Rather than directly optimizing densities on a grid, we instead optimize the parameters of a neural network which outputs those densities. This reparameterization leads to different and often better solutions. On a selection of 116 structural optimization tasks, our approach produces the best design 50% more often than the best baseline method.

Key facts. Cited by 44 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Sep 2019.

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Citing papers per year: 2021: 10; 2022: 10; 2023: 5; 2024: 8; 2025: 3; 2026: 8.

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  1. 2021Efficient and Modular Implicit Differentiationcited by 199
  2. 2021The Low-Rank Simplicity Bias in Deep Networkscited by 150
  3. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 88
  4. 2022Tutorial on amortized optimizationcited by 83
  5. 2021NTopo: Mesh-free Topology Optimization using Implicit Neural Representationscited by 41
  6. 2022Physical Design using Differentiable Learned Simulatorscited by 37
  7. 2021Variational Data Assimilation with a Learned Inverse Observation Operatorcited by 28
  8. 2021ICON: Learning Regular Maps Through Inverse Consistencycited by 26
  9. 2021Fast PDE-constrained optimization via self-supervised operator learningcited by 24
  10. 2022Topology Optimization via Machine Learning and Deep Learning: A Reviewcited by 22
  11. 2023Deep Learning in Deterministic Computational Mechanicscited by 21
  12. 2024Deep Diffusion Image Prior for Efficient OOD Adaptation in 3D Inverse Problemscited by 21
32 more
  1. 2024Neural topology optimization: the good, the bad, and the uglycited by 9
  2. 2022NCVX: A General-Purpose Optimization Solver for Constrained Machine and Deep Learningcited by 7
  3. 2021De-homogenization using Convolutional Neural Networkscited by 6
  4. 2023DMF-TONN: Direct Mesh-free Topology Optimization using Neural Networkscited by 6
  5. 2023Anatomically Constrained Implicit Face Modelscited by 4
  6. 2023Topology Optimization using Neural Networks with Conditioning Field Initialization for Improved Efficiencycited by 3
  7. 2024Neural Networks for Generating Better Local Optima in Topology Optimizationcited by 3
  8. 2021DNN-Based Topology Optimisation: Spatial Invariance and Neural Tangent Kernelcited by 2
  9. 2022Generative Thermal Design Through Boundary Representation and Multi-Agent Cooperative Environmentcited by 2
  10. 2024Gradient-free neural topology optimization: Towards effective fracture-resistant designscited by 2
  11. 2025Compliance Minimization via Physics-Informed Gaussian Processescited by 2
  12. 2024Multi-scale Topology Optimization using Neural Networkscited by 1
  13. 2024Pentagonal Photonic Crystal Mirrors: Scalable Lightsails with Enhanced Acceleration via Neural Topology Optimizationcited by 1
  14. 2024Generative Neural Reparameterization for Differentiable PDE-constrained Optimizationcited by 1
  15. 2026Multi-material Multi-physics Topology Optimization with Physics-informed Gaussian Process Priorscited by 1
  16. 2026KATOsuper: Surrogate-accelerated neural topology optimization with sensitivity-consistent Fourier neural operatorscited by 1
  17. 2021Discovery of Physics and Characterization of Microstructure from Data with Bayesian Hidden Physics Modelscited by 0
  18. 2021Improving Solar Cell Metallization Designs using Convolutional Neural Networkscited by 0
  19. 2022FRC-TOuNN: Topology Optimization of Continuous Fiber Reinforced Composites using Neural Networkcited by 0
  20. 2022Faster Optimization on Sparse Graphs via Neural Reparametrizationcited by 0
  21. 2022Deep convolutional surrogates and degrees of freedom in thermal designcited by 0
  22. 2022SELTO: Sample-Efficient Learned Topology Optimizationcited by 0
  23. 2023Bringing PDEs to JAX with forward and reverse modes automatic differentiationcited by 0
  24. 2024Structural Design Through Reinforcement Learningcited by 0
  25. 2025Diverse Topology Optimization using Modulated Neural Fieldscited by 0
  26. 2025On the Effect of Neural Field Reparameterization for 4DVARcited by 0
  27. 2026Generating Physically Sound Designs from Text and a Set of Physical Constraintscited by 0
  28. 2026Neural parametric representations for thin-shell shape optimisationcited by 0
  29. 2026Neural Operator-enabled Topology-informed Evolutionary Strategy for PDE-Constrained Optimizationcited by 0
  30. 2026Benchmarking Optimizers to Solve Inverse Problems with Differentiable Physics Simulatorscited by 0
  31. 2026HGTO: A Unified Graph-Based Physics-Informed Formulation for Structural Topology Optimizationcited by 0
  32. 2026Bilevel Optimization of Topology and Hyperparameters (BOTH)cited by 0