A novel ansatz-based physics-informed neural network for natural convection in semi-annular domains

We present a novel approach for modeling steady-state natural convection in deformed annular geometries using physics-informed neural networks (PINNs) enhanced with low-rank adaptation (LoRA). The solution ansatz enforces Dirichlet boundary conditions via a dedicated neural network trained independently from the main partial differential equations (PDE) solver, ensuring hard constraint satisfaction. Once the boundary is resolved, the PDE residual is minimized through LoRA, which updates only a low-rank subset of the main network's weights. This framework enables efficient generalization across geometries by decoupling boundary enforcement from the solution dynamics. We evaluate the method on a set of semi-elliptical domains with increasing deformation. While LoRA incurs increasing velocity error under strong geometric change, it consistently captures the global flow structure and temperature distribution. Compared to full PINN retraining, LoRA offers a substantial reduction in training time and computational cost, making it a promising strategy for rapid simulation and design workflows involving moderate-to-strong geometric variations.