שיטת פיזיקה-מודרנית להתמודדות עם נתוני קבוצה: בניית תיאוריות פונקציונליות מתקדמת עם התייחסות למשוואות Navier-Stokes

תקציר מקורי באנגליתarXiv:2609.39291v1 Announce Type: new Abstract: Physics-informed computational methods usually optimize parameters within a functional representation whose structure is fixed in advance. This work proposes a Physics-Informed Method of Group Data Handling (PI-GMDH), in which representations of coupled physical fields are progressively constructed during solution. Candidate functional directions are evaluated through the first variation of the complete physical and observational objective, introduced in packages, and followed by block-coordinate damped Gauss-Newton coefficient optimization. The framework is demonstrated with tensor-product Chebyshev functions on the incompressible Navier-Stokes equations using a two-dimensional time-dependent Taylor-Green benchmark. Under the tested configur