# Component-wise reduced order model lattice-type structure design

arXiv: https://arxiv.org/abs/2010.10770 · HTML: https://mlsanity.com/paper/2010.10770/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2020.

## Built on by (most cited first, 16 of 16)

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- [Thermodynamically Consistent Latent Dynamics Identification for Parametric Systems](https://mlsanity.com/paper/2506.08475/) (2025)
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- [Sequential decoder training for improved latent space dynamics identification](https://mlsanity.com/paper/2510.03535/) (2025)
- [Higher-Order LaSDI: Reduced Order Modeling with Multiple Time Derivatives](https://mlsanity.com/paper/2512.15997/) (2025)
- [Latent Space Element Method](https://mlsanity.com/paper/2601.01741/) (2026)
- [Efficient machine-learning surrogates for large-scale geological carbon and energy storage](https://mlsanity.com/paper/2310.07461/) (2023)
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## Abstract (arXiv)

Lattice-type structures can provide a combination of stiffness with light weight that is desirable in a variety of applications. Design optimization of these structures must rely on approximations of the governing physics to render solution of a mathematical model feasible. In this paper, we propose a topology optimization (TO) formulation that approximates the governing physics using component-wise reduced order modeling, which can reduce solution time by multiple orders of magnitude over a full-order finite element model while providing a relative error in the solution of less than one percent. In addition, the offline training data set from such component-wise models is reusable, allowing its application to many design problems for only the cost of a single offline training phase, and the component-wise method is nearly embarrassingly parallel. We also show how the parameterization chosen in our optimization allows a simplification of the component-wise reduced order model (CWROM) not noted in previous literature, for further speedup of the optimization process. The sensitivity of the compliance with respect to the particular parameterization is derived solely in the component level. In numerical examples, we demonstrate a 1000x speedup over a full-order FEM model with relative error of less than one percent and show minimum compliance designs for two different cantilever beam examples, one smaller and one larger. Finally, error bounds for displacement field, compliance, and compliance sensitivity of the CWROM are derived.