Multi-formulation isogeometric analysis and physics-informed machine learning for heat conduction in composite plates

Heat conduction in composite plates with geometric discontinuities presents persistent numerical challenges, including boundary approximation errors and discontinuous heat flux fields inherent to the finite element method (FEM). No multi-formulation framework has simultaneously benchmarked NURBS, Hierarchical B-Splines, and GRADED-NURBS isogeometric analysis (IGA) formulations against FEM for such problems. This paper addresses this gap by presenting a multi-formulation framework implementing three isogeometric formulations for steady-state and transient heat conduction, covering isotropic, orthotropic, and metal matrix composite laminates with and without circular cut-outs, validated against Fourier-series analytical benchmarks. Each isogeometric formulation provides C p−1 inter-element continuity and exact geometric representation of curved boundaries, two properties that Lagrangian FEM cannot deliver regardless of polynomial degree, resulting in equivalent or superior accuracy with substantially fewer degrees of freedom. Furthermore, to the best of our knowledge, power-law GRADED-NURBS refinement is applied for the first time to thermally loaded anisotropic composite plates with circular cut-outs, resolving steep thermal gradients near the hole using only 5% of the elements required by FEM. A Physics-Informed Machine Learning Surrogate (PIML) is additionally proposed as a physics-constrained surrogate for steady-state temperature prediction in perforated anisotropic plates. In contrast to purely data-driven models, the PIML enforces thermal boundary conditions exactly through its mathematical structure and embeds material anisotropy and domain geometry into the regression space, achieving R 2 = 0.9996 and a mean prediction error of 1.62 K across 81,178 simulation samples. All source code is publicly available at ( https://github.com/RahmouniFaouzi/IGA_FEM_ThermalAnalysis ).