# TopoMamba: A Load-Support Relation-Guided Multi-Directional State-Space Model for Topology Optimization

arXiv: https://arxiv.org/abs/2609.33688 · HTML: https://mlsanity.com/paper/2609.33688/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 26 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [VMamba: Visual State Space Model](https://mlsanity.com/paper/2401.10166/) (2024)
- [PlainMamba: Improving Non-Hierarchical Mamba in Visual Recognition](https://mlsanity.com/paper/2403.17695/) (2024)
- [Physics-Informed Diffusion Models](https://mlsanity.com/paper/2403.14404/) (2024)
- [Mamba-ND: Selective State Space Modeling for Multi-Dimensional Data](https://mlsanity.com/paper/2402.05892/) (2024)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain](https://mlsanity.com/paper/2003.04685/) (2020)
- [Neural networks for topology optimization](https://mlsanity.com/paper/1709.09578/) (2017)
- [On the use of Artificial Neural Networks in Topology Optimisation](https://mlsanity.com/paper/2208.02563/) (2022)
- [Topology Optimization via Machine Learning and Deep Learning: A Review](https://mlsanity.com/paper/2210.10782/) (2022)
- [On the Generalization in Topology Optimization via Sensitivity-Conditioned Bernoulli Flow Matching](https://mlsanity.com/paper/2606.02179/) (2026)
- [Physics-Informed Transformer for Real-Time High-Fidelity Topology Optimization](https://mlsanity.com/paper/2604.03522/) (2026)
- [HPG-Diff: Hierarchical physics-guided diffusion with differentiable connectivity constraints for topology optimization](https://mlsanity.com/paper/2607.07233/) (2026)

## Abstract (arXiv)

Deep learning has emerged as an efficient alternative for predicting high-performance material distributions in topology optimization. Existing methods struggle to accurately capture load-transfer information, limiting out-of-distribution generalization, while their model architectures often incur high computational costs. To address these challenges, this paper proposes TopoMamba, a topology prediction framework incorporating a load-support relation-guided multi-directional state-space model. Coupling physical fields with load-support relations enables more effective modeling of mechanical dependencies. A load-support relation-guided spatially adaptive fusion mechanism dynamically adjusts multi-directional scan features according to spatial conditions. Mamba is coupled with the solid isotropic material with penalty method to enhance structural mechanical performance while maintaining computational efficiency. Results on two-dimensional topology optimization benchmarks demonstrate that TopoMamba achieves superior topology prediction accuracy, out-of-distribution generalization, and computational efficiency over state-of-the-art models. The proposed load-support physics-guided framework enables efficient optimization of more complex structural systems.