# SELTO: Sample-Efficient Learned Topology Optimization

arXiv: https://arxiv.org/abs/2209.05098 · HTML: https://mlsanity.com/paper/2209.05098/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 59 references that are in the map.
- First posted on arXiv 12 Sep 2022.

## Builds on (most cited first, 27 of 27)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Road Extraction by Deep Residual U-Net](https://mlsanity.com/paper/1711.10684/) (2017)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [Learning Steerable Filters for Rotation Equivariant CNNs](https://mlsanity.com/paper/1711.07289/) (2017)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Generalization in Deep Learning](https://mlsanity.com/paper/1710.05468/) (2017)
- [Lorentz Group Equivariant Neural Network for Particle Physics](https://mlsanity.com/paper/2006.04780/) (2020)
- [Janossy Pooling: Learning Deep Permutation-Invariant Functions for Variable-Size Inputs](https://mlsanity.com/paper/1811.01900/) (2018)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain](https://mlsanity.com/paper/2003.04685/) (2020)
- [Geometric Deep Learning and Equivariant Neural Networks](https://mlsanity.com/paper/2105.13926/) (2021)
- [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)
- [Deep learning for determining a near-optimal topological design without any iteration](https://mlsanity.com/paper/1801.05463/) (2018)
- [Neural networks for topology optimization](https://mlsanity.com/paper/1709.09578/) (2017)
- [3D Topology Optimization using Convolutional Neural Networks](https://mlsanity.com/paper/1808.07440/) (2018)
- [A Novel Topology Optimization Approach using Conditional Deep Learning](https://mlsanity.com/paper/1901.04859/) (2019)
- [A deep Convolutional Neural Network for topology optimization with strong generalization ability](https://mlsanity.com/paper/1901.07761/) (2019)
- [Segmentation Loss Odyssey](https://mlsanity.com/paper/2005.13449/) (2020)
- [Robustness of Rotation-Equivariant Networks to Adversarial Perturbations](https://mlsanity.com/paper/1802.06627/) (2018)
- [A New CGAN Technique for Constrained Topology Design Optimization](https://mlsanity.com/paper/1901.07675/) (2019)

## Abstract (arXiv)

Recent developments in Deep Learning (DL) suggest a vast potential for Topology Optimization (TO). However, while there are some promising attempts, the subfield still lacks a firm footing regarding basic methods and datasets. We aim to address both points. First, we explore physics-based preprocessing and equivariant networks to create sample-efficient components for TO DL pipelines. We evaluate them in a large-scale ablation study using end-to-end supervised training. The results demonstrate a drastic improvement in sample efficiency and the predictions' physical correctness. Second, to improve comparability and future progress, we publish the two first TO datasets containing problems and corresponding ground truth solutions.