Modular fine-tuning of physics-informed neural networks for natural convection in eccentric geometries

Physics-informed neural networks (PINNs) have emerged as promising tools for solving partial differential equations (PDEs) in complex domains, yet their adaptation to geometrically varying configurations remains computationally demanding. This work introduces a modular transfer learning framework for PINNs that combines boundary-aware pretraining, intermediate fine-tuning, and a lightweight geometry-specific correction layer. The method enforces Dirichlet boundary conditions through hard constraints to ensure physical consistency across geometries. Natural convection in eccentric annuli is selected as a benchmark case to assess performance against computational fluid dynamics ground truth over a range of geometric perturbations. Lightweight fine-tuning achieves temperature prediction errors below 2% in moderately perturbed cases while preserving coherent flow and thermal structures under significant domain shifts. Compared to full fine-tuning, the proposed approach reduces trainable parameters and training time by a substantial margin, making it suitable for rapid deployment in surrogate modeling and digital twin applications. The results underscore the framework's capacity for efficient and accurate generalization across geometrical variations in PDE-based simulations.