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[Submitted on 14 Oct 2026] Title:Learning Topology-Aware Representations for Mechanics-Relevant TPMS Metamaterials View a PDF of the paper titled Learning Topology-Aware Representations for Mechanics-Relevant TPMS Metamaterials, by Songlin Duan and 3 other authors View PDF HTML (experimental) Abstract:Learning informative representations of mechanical Triply Periodic Minimal Surface (TPMS) metamaterials is important for mechanics analysis and structural design, yet existing methods have rarely explicitly supervised learned representations with information about global structural connectivity that is relevant to mechanical response. We propose a topology-aware representation learning framework that integrates persistent homology into a DMAE backbone to explicitly encode global structural connectivity. A persistence-guided masking strategy prioritizes patches associated with persistent topological features, while an auxiliary persistent-homology decoder encourages the latent representation to retain information about topological feature counts across connected components, tunnels, and voids. We evaluate the learned representations on two complementary TPMS datasets using family classification, mechanical-property classification, unsupervised clustering, and regression. Across the two datasets, our method demonstrates strong performance in both structural family and mechanical-property classification, improving family classification by up to 3.9% while achieving the best linear-probe performance. More notably, unsupervised property-clustering performance improves by up to 26.7% and 51.5% across the two datasets, while strong regression performance is retained with $R^2=0.993$. These results establish persistent topology as an effective inductive bias for representation learning of complex three-dimensional mechanical metamaterials. Comments: 29 pages, 10 figures Subjects: Machine Learning (cs.LG); Computational Engineering, Finance, and Science (cs.CE); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (stat.ML) Cite as: arXiv:2610.20684 [cs.LG] (or arXiv:2610.20684v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2610.20684 arXiv-issued DOI via DataCite Submission history From: Songlin Duan [view email] [v1] Wed, 14 Oct 2026 16:38:20 UTC (11,809 KB) Full-text links: Access Paper: View a PDF of the paper titled Learning Topology-Aware Representations for Mechanics-Relevant TPMS Metamaterials, by Songlin Duan and 3 other authors View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.LG new | recent | 2026-10 Change to browse by: cs cs.CE cs.CV stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)