Surrogate models for diffusion on graphs via sparse polynomials

[2502.06595] Surrogate models for diffusion on graphs via sparse polynomials Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2502.06595 (math) [Submitted on 10 Feb 2025 ( v1 ), last revised 13 Apr 2026 (this version, v3)] Title: Surrogate models for diffusion on graphs via sparse polynomials Authors: Giuseppe Alessio D'Inverno , Kylian Ajavon , Simone Brugiapaglia View a PDF of the paper titled Surrogate models for diffusion on graphs via sparse polynomials, by Giuseppe Alessio D'Inverno and Kylian Ajavon and Simone Brugiapaglia View PDF HTML (experimental) Abstract: Diffusion kernels over graphs have been widely utilized as effective tools in various applications due to their ability to accurately model the flow of information through nodes and edges. However, there is a notable gap in the literature regarding the development of surrogate models for diffusion processes on graphs. In this work, we fill this gap by proposing sparse polynomial-based surrogate models for parametric diffusion equations on graphs with community structure. In tandem, we provide convergence guarantees for both least squares and compressed sensing-based approximations by showing the holomorphic regularity of parametric solutions to these diffusion equations. Our theoretical findings are accompanied by a series of numerical experiments conducted on both synthetic and real-world graphs that demonstrate the applicability of our methodology. Subjects: Numerical Analysis (math.NA) ; Machine Learning (cs.LG) MSC classes: 34B45, 41A10, 41A63, 65D40 Cite as: arXiv:2502.06595 [math.NA] (or arXiv:2502.06595v3 [math.NA] for this version) https://doi.org/10.48550/arXiv.2502.06595 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Giuseppe Alessio D'Inverno [ view email ] [v1] Mon, 10 Feb 2025 15:57:33 UTC (2,275 KB) [v2] Tue, 30 Sep 2025 10:12:53 UTC (975 KB) [v3] Mon, 13 Apr 2026 19:36:37 UTC (992 KB) Full-text links: Access Paper: View a PDF of the paper titled Surrogate models for diffusion on graphs via sparse polynomials, by Giuseppe Alessio D'Inverno and Kylian Ajavon and Simone Brugiapaglia View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2025-02 Change to browse by: cs cs.LG cs.NA math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark 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? ) 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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