נוזלים שאתה יכול להסתמך עליהם: למידת פעולות שמשמרות תכונות לתאוצות אינקומפרסיביות

תקציר מקורי באנגליתarXiv:2602.15472v5 Announce Type: replace-cross Abstract: We present a novel property-preserving kernel-based operator learning method for incompressible flows governed by the incompressible Navier--Stokes equations. Traditional numerical solvers incur significant computational costs to respect incompressibility. Operator learning offers efficient surrogate models, but current neural operators fail to exactly enforce physical properties such as incompressibility, periodicity, and turbulence. Our kernel method maps input functions to expansion coefficients of output functions in a property-preserving kernel basis, ensuring that predicted velocity fields \emph{analytically} and \emph{simultaneously} preserve the aforementioned physical properties. We present universal approximation results a