# GUST: Quantifying Free-Form Geometric Uncertainty of Metamaterials Using Small Data

arXiv: https://arxiv.org/abs/2506.12051 · HTML: https://mlsanity.com/paper/2506.12051/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 49 references that are in the map.
- First posted on arXiv 28 May 2025.

## Builds on (most cited first, 30 of 30)

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- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Semantic Image Synthesis with Spatially-Adaptive Normalization](https://mlsanity.com/paper/1903.07291/) (2019)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Revisiting Unreasonable Effectiveness of Data in Deep Learning Era](https://mlsanity.com/paper/1707.02968/) (2017)
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- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [CNN Features off-the-shelf: an Astounding Baseline for Recognition](https://mlsanity.com/paper/1403.6382/) (2014)
- [Scaling Laws for Transfer](https://mlsanity.com/paper/2102.01293/) (2021)
- [Explicit Inductive Bias for Transfer Learning with Convolutional Networks](https://mlsanity.com/paper/1802.01483/) (2018)
- [FreeU: Free Lunch in Diffusion U-Net](https://mlsanity.com/paper/2309.11497/) (2023)
- [What makes ImageNet good for transfer learning?](https://mlsanity.com/paper/1608.08614/) (2016)
- [DiffFit: Unlocking Transferability of Large Diffusion Models via Simple Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2304.06648/) (2023)
- [A Closer Look at Few-shot Image Generation](https://mlsanity.com/paper/2205.03805/) (2022)
- [One-Shot Generative Domain Adaptation](https://mlsanity.com/paper/2111.09876/) (2021)
- [Few-shot Image Generation with Diffusion Models](https://mlsanity.com/paper/2211.03264/) (2022)
- [Generalized One-shot Domain Adaptation of Generative Adversarial Networks](https://mlsanity.com/paper/2209.03665/) (2022)
- [Transfer Learning for Diffusion Models](https://mlsanity.com/paper/2405.16876/) (2024)
- [GAN-DUF: Hierarchical Deep Generative Models for Design Under Free-Form Geometric Uncertainty](https://mlsanity.com/paper/2202.10558/) (2022)
- [Image Synthesis under Limited Data: A Survey and Taxonomy](https://mlsanity.com/paper/2307.16879/) (2023)
- [An Empirical Study of Scaling Laws for Transfer](https://mlsanity.com/paper/2408.16947/) (2024)
- [Mechanical Cloak via Data-Driven Aperiodic Metamaterial Design](https://mlsanity.com/paper/2107.13147/) (2021)
- [Provable Sample-Efficient Transfer Learning Conditional Diffusion Models via Representation Learning](https://mlsanity.com/paper/2502.04491/) (2025)
- [Uncertainty quantification of microstructure variability and mechanical behaviour of additively manufactured lattice structures](https://mlsanity.com/paper/2103.09550/) (2021)

## Abstract (arXiv)

This paper introduces GUST (Generative Uncertainty learning via Self-supervised pretraining and Transfer learning), a framework for quantifying free-form geometric uncertainties inherent in the manufacturing of metamaterials. GUST leverages the representational power of deep generative models to learn a high-dimensional conditional distribution of as-fabricated unit cell geometries given nominal designs, thereby enabling uncertainty quantification. To address the scarcity of real-world manufacturing data, GUST employs a two-stage learning process. First, it leverages self-supervised pretraining on a large-scale synthetic dataset to capture the structure variability inherent in metamaterial geometries and an approximated distribution of as-fabricated geometries given nominal designs. Subsequently, GUST employs transfer learning by fine-tuning the pretrained model on limited real-world manufacturing data, allowing it to adapt to specific manufacturing processes and nominal designs. With only 960 unit cells additively manufactured in only two passes, GUST can capture the variability in geometry and effective material properties. In contrast, directly training a generative model on the same amount of real-world data proves insufficient, as demonstrated through both qualitative and quantitative comparisons. This scalable and cost-effective approach significantly reduces data requirements while maintaining the effectiveness in learning complex, real-world geometric uncertainties, offering an affordable method for free-form geometric uncertainty quantification in the manufacturing of metamaterials. The capabilities of GUST hold significant promise for high-precision industries such as aerospace and biomedical engineering, where understanding and mitigating manufacturing uncertainties are critical.