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Poster by M. Granfors at the Learning on graphs and geometry meetup in Uppsala, 11 February 2025

GAUDI leverages a hierarchical graph-convolutional variational autoencoder architecture, where an encoder progressively compresses the graph into a low-dimensional latent space, and a decoder reconstructs the graph from the latent embedding. (Image by M. Granfors and J. Pineda.)
Global graph features unveiled by unsupervised geometric deep learning
Mirja Granfors, Jesús Pineda, Blanca Zufiria Gerbolés, Daniel Vereb, Joana B. Pereira, Carlo Manzo, and Giovanni Volpe
Learning on graphs and geometry meetup at Uppsala University
Date: 11 February 2025
Place: Uppsala university

Graphs are used to model complex relationships, such as interactions between particles or connections between brain regions. The structural complexity and variability of graphs pose challenges to their efficient analysis and classification. Here, we propose GAUDI (Graph Autoencoder Uncovering Descriptive Information), a graph autoencoder that addresses these challenges. GAUDI’s encoder progressively reduces the size of the graph using multi-step hierarchical pooling, while its decoder incrementally increases the graph size until the original dimensions are restored, focusing on the node and edge features while preserving the graph structure through skip-connections. By training GAUDI to minimize the difference between the node and edge features of the input graph and those of the output graph, it is compelled to capture the most critical parameters describing these features in the latent space, thereby enabling the extraction of essential parameters characterizing the graphs. We demonstrate the performance of GAUDI across diverse graph data originating from complex systems, including the estimation of the parameters of Watts-Strogatz graphs, the classification of protein assembly structures from single-molecule localization microscopy data, the analysis of collective behaviors, and correlations between brain connections and age. This approach offers a robust framework for efficiently analyzing and interpreting complex graph data, facilitating the extraction of meaningful patterns and insights across a wide range of applications.

Roadmap on machine learning glassy dynamics published in Nature Review Physics

Visual summary of the scope of the review. (Image by the Authors.)
Roadmap on machine learning glassy dynamics
Gerhard Jung, Rinske M. Alkemade, Victor Bapst, Daniele Coslovich, Laura Filion, François P. Landes, Andrea J. Liu, Francesco Saverio Pezzicoli, Hayato Shiba, Giovanni Volpe, Francesco Zamponi, Ludovic Berthier & Giulio Biroli
Nature Review Physics (2025)
doi: 10.1038/s42254-024-00791-4
arxiv: 2311.14752

Unravelling the connections between microscopic structure, emergent physical properties and slow dynamics has long been a challenge when studying the glass transition. The absence of clear visible structural order in amorphous configurations complicates the identification of the key physical mechanisms underpinning slow dynamics. The difficulty in sampling equilibrated configurations at low temperatures hampers thorough numerical and theoretical investigations. We explore the potential of machine learning (ML) techniques to face these challenges, building on the algorithms that have revolutionized computer vision and image recognition. We present both successful ML applications and open problems for the future, such as transferability and interpretability of ML approaches. To foster a collaborative community effort, we also highlight the ‘GlassBench’ dataset, which provides simulation data and benchmarks for both 2D and 3D glass formers. We compare the performance of emerging ML methodologies, in line with benchmarking practices in image and text recognition. Our goal is to provide guidelines for the development of ML techniques in systems displaying slow dynamics and inspire new directions to improve our theoretical understanding of glassy liquids.