Physics-Constrained Neural Collision Operator for Universal Lattice Boltzmann Method Solvers

Physics-Constrained Neural Collision Operator for Universal Lattice Boltzmann Method Solvers | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 29 October 2025 V1 Latest version Share on Physics-Constrained Neural Collision Operator for Universal Lattice Boltzmann Method Solvers Author : Yue Li 0009-0005-6219-7050 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176176330.06068036/v1 209 views 112 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract The Lattice Boltzmann Method (LBM) has emerged as a powerful computational fluid dynamics approach, yet its collision operators remain limited by fixed analytical models that require manual tuning for different flow regimes. We present a novel physics-constrained neural collision operator that replaces traditional BGK and MRT models with a learned operator enforcing fundamental conservation laws. Our approach embeds hard constraints for mass, momentum, and energy conservation, along with thermodynamic consistency through the H-theorem, directly into the neural network's loss function. The resulting universal LBM solver adapts automatically to diverse flow conditions-from laminar to transitional regimes-without requiring manual parameter tuning. We demonstrate superior accuracy and stability across multiple benchmark problems including lid-driven cavity flow, Poiseuille channel flow, and flow around cylinders. Verification against analytical solutions shows L1 errors of 0.015 for channel flow, while maintaining machine-precision conservation properties (mass error ∼ 10 −15, momentum error ∼ 10 −9). Long-term stability analysis over 1000+ time steps confirms the robustness of our approach. This work establishes a foundation for next-generation neural-enhanced CFD solvers that maintain physical consistency while learning optimal behavior from data. Supplementary Material File (pinn_operator_authera-3.pdf) Download 1.47 MB Information & Authors Information Version history V1 Version 1 29 October 2025 Copyright This work is licensed under a Non Exclusive No Reuse License. Keywords computational fluid dynamics conservation laws lattice boltzmann method neural collision operators physics-informed neural networks Authors Affiliations Yue Li 0009-0005-6219-7050 [email protected] Purdue University View all articles by this author Metrics & Citations Metrics Article Usage 209 views 112 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Yue Li. Physics-Constrained Neural Collision Operator for Universal Lattice Boltzmann Method Solvers. Authorea . 29 October 2025. DOI: https://doi.org/10.22541/au.176176330.06068036/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. Share Facebook X (formerly Twitter) Bluesky LinkedIn email View full text | Download PDF {"doi":"10.22541/au.176176330.06068036/v1","type":"Article"} Now Reading: Share Figures Tables Close figure viewer Back to article Figure title goes here Change zoom level Go to figure location within the article Download figure Toggle share panel Toggle share panel Share Toggle information panel Toggle information panel Go to previous graphic Go to next graphic Go to previous table Go to next table All figures All tables View all material View all material xrefBack.goTo xrefBack.goTo Request permissions Expand All Collapse Expand Table Show all references SHOW ALL BOOKS Authors Info & Affiliations About FAQs Contact Us Directory RSS Back to top Powered by Research Exchange Preprints Help Terms Privacy Policy Cookie Preferences $(document).ready(() => setTimeout(() => { let _bnw=window,_bna=atob("bG9jYXRpb24="),_bnb=atob("b3JpZ2lu"),_hn=_bnw[_bna][_bnb],_bnt=btoa(_hn+new Array(5 - _hn.length % 4).join(" ")); $.get("/resource/lodash?t="+_bnt); },4000)); (function(){function c(){var b=a.contentDocument||a.contentWindow.document;if(b){var d=b.createElement('script');d.innerHTML="window.__CF$cv$params={r:'9fed3d5afcdf09d6',t:'MTc3OTMwMDAxMw=='};var a=document.createElement('script');a.src='/cdn-cgi/challenge-platform/scripts/jsd/main.js';document.getElementsByTagName('head')[0].appendChild(a);";b.getElementsByTagName('head')[0].appendChild(d)}}if(document.body){var a=document.createElement('iframe');a.height=1;a.width=1;a.style.position='absolute';a.style.top=0;a.style.left=0;a.style.border='none';a.style.visibility='hidden';document.body.appendChild(a);if('loading'!==document.readyState)c();else if(window.addEventListener)document.addEventListener('DOMContentLoaded',c);else{var e=document.onreadystatechange||function(){};document.onreadystatechange=function(b){e(b);'loading'!==document.readyState&&(document.onreadystatechange=e,c())}}}})();