# Inferring topological transitions in pattern-forming processes with self-supervised learning

arXiv: https://arxiv.org/abs/2203.10204 · HTML: https://mlsanity.com/paper/2203.10204/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 72 references that are in the map.
- First posted on arXiv 19 Mar 2022.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [One weird trick for parallelizing convolutional neural networks](https://mlsanity.com/paper/1404.5997/) (2014)
- [Understanding the Role of Individual Units in a Deep Neural Network](https://mlsanity.com/paper/2009.05041/) (2020)
- [Concrete Dropout](https://mlsanity.com/paper/1705.07832/) (2017)
- [Multi-task Self-Supervised Visual Learning](https://mlsanity.com/paper/1708.07860/) (2017)
- [Triple descent and the two kinds of overfitting: Where & why do they appear?](https://mlsanity.com/paper/2006.03509/) (2020)
- [Discovering Phase Transitions with Unsupervised Learning](https://mlsanity.com/paper/1606.00318/) (2016)
- [Unsupervised learning of phase transitions: from principal component analysis to variational autoencoders](https://mlsanity.com/paper/1703.02435/) (2017)
- [Learning Disordered Topological Phases by Statistical Recovery of Symmetry](https://mlsanity.com/paper/1709.05790/) (2017)

## Built on by (most cited first, 1 of 1)

- [Multiscale geometrical and topological learning in the analysis of soft matter collective dynamics](https://mlsanity.com/paper/2507.21265/) (2025)

## Abstract (arXiv)

The identification and classification of transitions in topological and microstructural regimes in pattern-forming processes are critical for understanding and fabricating microstructurally precise novel materials in many application domains. Unfortunately, relevant microstructure transitions may depend on process parameters in subtle and complex ways that are not captured by the classic theory of phase transition. While supervised machine learning methods may be useful for identifying transition regimes, they need labels which require prior knowledge of order parameters or relevant structures describing these transitions. Motivated by the universality principle for dynamical systems, we instead use a self-supervised approach to solve the inverse problem of predicting process parameters from observed microstructures using neural networks. This approach does not require predefined, labeled data about the different classes of microstructural patterns or about the target task of predicting microstructure transitions. We show that the difficulty of performing the inverse-problem prediction task is related to the goal of discovering microstructure regimes, because qualitative changes in microstructural patterns correspond to changes in uncertainty predictions for our self-supervised problem. We demonstrate the value of our approach by automatically discovering transitions in microstructural regimes in two distinct pattern-forming processes: the spinodal decomposition of a two-phase mixture and the formation of concentration modulations of binary alloys during physical vapor deposition of thin films. This approach opens a promising path forward for discovering and understanding unseen or hard-to-discern transition regimes, and ultimately for controlling complex pattern-forming processes.