mlsanityData to 7 Oct 2026

DNN-Based Topology Optimisation: Spatial Invariance and Neural Tangent Kernel

arXiv 2106.05710 ↗First posted 10 Jun 2021stat.ML cs.LGcited by 2

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Abstract (arXiv)

We study the Solid Isotropic Material Penalisation (SIMP) method with a density field generated by a fully-connected neural network, taking the coordinates as inputs. In the large width limit, we show that the use of DNNs leads to a filtering effect similar to traditional filtering techniques for SIMP, with a filter described by the Neural Tangent Kernel (NTK). This filter is however not invariant under translation, leading to visual artifacts and non-optimal shapes. We propose two embeddings of the input coordinates, which lead to (approximate) spatial invariance of the NTK and of the filter. We empirically confirm our theoretical observations and study how the filter size is affected by the architecture of the network. Our solution can easily be applied to any other coordinates-based generation method.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 17 of its 35 references that are in the map. First posted on arXiv 10 Jun 2021.

Builds on

17 of 35 references.

References · 17

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5 more
  1. 2017Neural networks for topology optimizationcited by 39
  2. 2019Global optimization of dielectric metasurfaces using a physics-driven neural networkcited by 30
  3. 20183D Topology Optimization using Convolutional Neural Networkscited by 27
  4. 2019Disentangling Trainability and Generalization in Deep Neural Networkscited by 16
  5. 2019A New CGAN Technique for Constrained Topology Design Optimizationcited by 5

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Cited by year

Citing papers per year: 2022: 1; 2023: 0; 2024: 1.

2 papers.

  1. 2022Neural Tangent Kernel: A Surveycited by 22
  2. 2024Neural topology optimization: the good, the bad, and the uglycited by 9