# Neural parametric representations for thin-shell shape optimisation

arXiv: https://arxiv.org/abs/2604.06612 · HTML: https://mlsanity.com/paper/2604.06612/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 42 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Builds on (most cited first, 13 of 13)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Neural reparameterization improves structural optimization](https://mlsanity.com/paper/1909.04240/) (2019)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [Surface Extraction from Neural Unsigned Distance Fields](https://mlsanity.com/paper/2309.08878/) (2023)
- [Neural topology optimization: the good, the bad, and the ugly](https://mlsanity.com/paper/2407.13954/) (2024)
- [Infill topology and shape optimisation of lattice-skin structures](https://mlsanity.com/paper/2105.04017/) (2021)
- [Isogeometric shape optimisation of shell structures using multiresolution subdivision surfaces](https://mlsanity.com/paper/1605.06288/) (2016)
- [Interrogation of spline surfaces with application to isogeometric design and analysis of lattice-skin structures](https://mlsanity.com/paper/1810.07982/) (2018)
- [Automated shape and thickness optimization for non-matching isogeometric shells using free-form deformation](https://mlsanity.com/paper/2308.03781/) (2023)
- [Shell topology optimization based on level set method](https://mlsanity.com/paper/2401.13868/) (2024)

## Abstract (arXiv)

Shape optimisation of thin-shell structures requires a flexible, differentiable geometric representation suitable for gradient-based optimisation. We propose a neural parametric geometry representation (NRep) for shells based on a neural network with periodic activation functions. The NRep is defined using a multi-layer perceptron (MLP), which maps the parametric coordinates of mid-surface vertices to their physical coordinates. A structural compliance optimisation problem is posed to optimise the shape of a thin-shell parameterised by the NRep subject to a volume constraint, with the network parameters as design variables. The resulting shape optimisation problem is solved using a gradient-based optimisation algorithm. Benchmark examples with classical solutions and comparisons with the free-form deformation method demonstrate that the proposed NRep is capable of representing shell geometries with local geometric features using a small set of network parameters. The robustness of the approach has been demonstrated with different initial geometries, boundary conditions and neural network hyperparameters. The approach also exhibits potential for complex lattice-skin structures, owing to the compact and expressive geometry representation afforded by the NRep.