Parameter-efficient transfer of physics-informed neural networks for buoyancy-driven enclosures via geometry-conditioned adapters

We study rapid geometric transfer for physics-informed neural networks (PINNs) in buoyancy-driven cavity flows with an inner heated cylinder. Small eccentricities of the cylinder reshape the thermal layer and the rising plume, which makes wall heat transfer a stringent test. We propose a geometry-aware adapter augmented PINN (GeoAda-PINN) that conditions a frozen backbone on explicit geometric descriptors and signed distance features while updating only compact residual adapters during transfer. Training uses a hybrid strong and weak objective with plume-aware collocation. For vertical and horizontal offsets, we compare computational fluid dynamics (CFD), a Vanilla-PINN retrained per geometry, and GeoAda-PINN. Temperature and velocity fields and mean Nusselt numbers on inner and outer walls indicate that the Vanilla-PINN most closely matches CFD on the hardest inner wall cases, while the GeoAda-PINN achieves competitive accuracy with markedly fewer updated parameters and shorter fine-tunes. An accuracy and time frontier shows the GeoAda-PINN reaching within about 5% mean absolute percent error of the inner wall Nusselt in substantially less wall clock time. These results support parameter-efficient and geometry-conditioned adapters as a practical path to scalable PINN surrogates in multi-query convection problems.