Writhe-Based Polymer Link Classification Using Machine Learning

Jack Beda; Djordje Mihajlovic; Kasturi Barkataki; Davide Michieletto

math.GTJul 22, 2026

Writhe-Based Polymer Link Classification Using Machine Learning

Authors: Jack Beda, Djordje Mihajlovic, Kasturi Barkataki, Davide Michieletto

Organizations: School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK. · School of Mathematics, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, UK. · MRC Human Genetics Unit, Institute of Genetics and Cancer, University of Edinburgh, Edinburgh EH4 2XU, UK

Abstract

Unique and rapid classification of knots and links is an open mathematical problem that is relevant to a range of (bio)physical systems, including polymer melts, DNA, and proteins. In this paper, we explore a data-driven approach to the classification problem of link topology. Extending the framework introduced in Ref. 1 (Sleiman et al, 2024 Soft Matter, 20(1), pp.71-78), we show that a feedforward neural network trained on the writhe density matrix classifies thermally equilibrated configurations of the first six prime links with 97% accuracy. We demonstrate that this accuracy remains high across a range of temperatures and lengths of link components, while rapidly deteriorating with the addition of topology-altering Gaussian noise; a result consistent with the writhe density matrix containing features sensitive to topology. Our results show that neural networks based on the writhe density matrix efficiently classify two-component links, establishing machine learning as a promising tool for rapid classification of more complex link topologies, e.g. Borromean rings and multi-component links, as the computational cost of exact numerical calculation of topological invariants becomes prohibitive.

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May 11, 2026 · cs.LGJ/K move · Enter open · S save

It's All Connected: Topology-Aware Structural Graph Encoding Improves Performance on Polymer Prediction

H. Ibrahim Erdogan, Punith Raviswamy, Nikita Agrawal, Yannik Köster+4

University of Bayreuth, Germany · Faculty of Engineering Science, University of Bayreuth, Germany · Faculty of Mathematics, Physics & Computer Science, University of Bayreuth, Germany · Friedrich Schiller University Jena, Germany · Laboratory of Organic and Macromolecular Chemistry (IOMC), Friedrich Schiller University Jena, Germany

Graph Neural Networks (GNNs) have achieved strong results in molecular property prediction, but polymers present distinct challenges: labeled datasets are scarce and small (typically in the order of hundreds of polymers) due to the need for expensive experimentation, and complex polymer chain distributions influence polymer properties. Established practice in polymer prediction represents polymers solely by graphs of their repeat units, discarding the chain-scale morphology that governs key properties such as the glass transition temperature (

T_g

). In this work, we propose a principled graph construction that addresses this gap. Given a polymer's molecular mass distribution (MMD), we sample representative chains from the Schulz-Zimm distribution and construct representative sets of large graphs encoding chain-scale topology directly, with atoms and bonds featurized using rich chemical descriptors. We further pretrain GNN encoders via masked graph modeling on 100,000 unlabeled PSMILES strings before fine-tuning on labeled data. On a dataset of 381 polymers (180 homopolymers and 201 copolymers), we show that graph construction and self-supervised pretraining are jointly necessary: without pretraining, the large graph method matches the repeat-unit baseline (28.40 K vs. 28.36 K RMSE); with pretraining, it achieves 24.76 K +/- 3.30 K, a 5.1% reduction in mean error over the pretrained repeat-unit baseline (26.08 K +/- 4.20 K, p < 0.001, 30 runs). An ablation removing chemical features degrades performance to 36.65 K, confirming both components are essential. Results are architecture-agnostic, holding for both GINE and GATv2 encoders.

Polymer Graph Neural Networks Molecular Property Prediction Topological Data Analysis

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Abstract

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