Efficient self-attention-based emulation of gravitational-wave spectrum with full parameter space exploration

Efficient self-attention-based emulation of gravitational-wave spectrum with full parameter space exploration | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Efficient self-attention-based emulation of gravitational-wave spectrum with full parameter space exploration Bohua Li, Fan Zhang, Yifang Luo, Joel Meyers, Paul Shapiro, Erik Katsavounidis This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8253597/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Fast emulation of sequential data generated by numerical computations is vital for large-scale Bayesian analysis in cosmology and astrophysics. Despite the success of neural network models in such tasks, benchmarks typically fall short of the required sub-percent accuracy and lack generalizability to broader data sets of different features and physical origins. Here we introduce SageNet+, a physics-informed framework for emulating gravitational-wave spectrum, while our self-attention-based design is adaptable to generic sequential data. First-principles modeling of the stochastic gravitational-wave background from cosmic inflation takes tens of seconds per evaluation to solve differential integrations. Instead, our SageNet+ emulator can predict the present-day gravitational-wave spectrum in less than 10 ms for every set of the nine cosmological parameters with wide prior ranges, achieving a thousand-fold speed-up over numerical methods. Based on the Transformer architecture, SageNet+ combines learnable positional embeddings and adaptive sequence standardization to preserve spectral features. We further employ refined data preprocessing to maximize physical information and devise novel metrics to assess model performance. Trained on 180,000 spectra that explore the full parameter space, SageNet+ attains sub-percent accuracy for all test data. This enables real-time parameter inferences and joint analyses with external data. SageNet+ presents an optimal, systematic and generalizable framework for emulation tasks in physical sciences. Physical sciences/Astronomy and planetary science/Astronomy and astrophysics/Cosmology Physical sciences/Astronomy and planetary science/Astronomy and astrophysics/General relativity and gravity Full Text Additional Declarations There is NO Competing Interest. Supplementary Files Supplementaryinformation.pdf Physical model and numerical algorithms for GW spectra Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8253597","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":588992633,"identity":"d30596e0-6a41-4866-8cae-f73dede4e437","order_by":0,"name":"Bohua 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