Neural Network based Prediction on Equation of State with Physical Constraints

Neural Network based Prediction on Equation of State with Physical Constraints | 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 Neural Network based Prediction on Equation of State with Physical Constraints Dongyang Kuang, Shiwei Li, Buxuan Wang, Chao Xiong, Shichang Zhang, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5350620/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 25 Jul, 2025 Read the published version in Scientific Reports → Version 1 posted 8 You are reading this latest preprint version Abstract The equation of state (EOS) is essential for understanding material behavior under different pressure-temperature-volume (P-T-V) conditions across various disciplines. Traditional models, such as the Mie-Gruneisen-Debye equation, rely on thermodynamic assumptions and expert knowledge, while classical Gaussian process based machine learning approaches can be sensitive to choice of kernels and are limited by scalability and extrapolability. To overcome these limitations, we propose a neural network based physics informed deep learning method (EOSNN) that jointly learns multiple EOS surfaces from diverse data sources, including static and dynamic compression and ab initio calculations. Additionally, a probabilistic model is developed to account for both aleatoric and epistemic uncertainties. Our numerical experiments show that EOSNN outperforms traditional and Gaussian process methods in several aspects including accuracy, robustness and extensibility. Particularly on the challenging partially supervised task where energy information is limited on part of the Hugoniot curve, our method’s prediction for the energy off-Hugoniot can still reach a R2 score as high as 0.83, correlation coefficient greater than 0.95 and RMSE as low as 0.52 eV/atom with proper selection of regularization for physical consistency. This result is even slightly better than the fully supervised case for traditional regression method based on the Mie-Gruneisen equation. These benefits can be further enhanced with physics-informed regularizations on quantities such as heat capacity (CV), Gruneisen parameter (γ) or bulk modulus (KT). Physical sciences/Physics/Statistical physics thermodynamics and nonlinear dynamics/Thermodynamics Physical sciences/Mathematics and computing Physical sciences/Materials science/Theory and computation/Computational methods Earth and environmental sciences/Solid earth sciences Earth and environmental sciences/Planetary science Physical sciences/Astronomy and planetary science/Planetary science Full Text Additional Declarations No competing interests reported. Supplementary Files SupplementTable.xlsx SupplementaryInfo.pdf Cite Share Download PDF Status: Published Journal Publication published 25 Jul, 2025 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 02 Jun, 2025 Reviews received at journal 30 May, 2025 Reviewers agreed at journal 26 Apr, 2025 Reviews received at journal 24 Apr, 2025 Reviewers agreed at journal 24 Apr, 2025 Reviewers invited by journal 24 Apr, 2025 Submission checks completed at journal 23 Apr, 2025 First submitted to journal 13 Apr, 2025 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. 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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-5350620","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":447549273,"identity":"9798059d-beb6-427e-9dee-1f5502cf14ca","order_by":0,"name":"Dongyang 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