Mixed convection physical-informed neural networks for flow reconstruction with sparse thermal data and partial physics in a lid-driven cavity

Accurate reconstruction of convective heat transfer mechanisms remains a significant challenge in thermal engineering, particularly for ill-posed inverse problems with incomplete boundary conditions. Conventional numerical methods, including finite element method and finite volume approaches, often struggle with solution uniqueness and numerical stability under these ill-posed conditions. In contrast, physics-informed neural networks offer a promising alternative by integrating sparse data with physical conservation laws. In this study, we proposed a novel mixed convection physics-informed neural network (MC-PINN) framework for flow field reconstruction in mixed convection heat transfer problems, utilizing sparse temperature measurements and partial physical constraints. To enhance its ability to capture multi-scale flow features, the MC-PINN framework incorporates Fourier feature embeddings and an augmented Lagrangian method, which dynamically adjusts the loss function weights during training. Bayesian inference is employed for hyperparameter optimization, enhancing model accuracy in handling complex flows. Numerical experiments demonstrate that the proposed MC-PINN can accurately reconstruct the velocity field with a coefficient of determination R2 > 99% using only 0.1% sparse thermal measurements, and it exhibits strong robustness to data noise. Compared to the vanilla PINN, the MC-PINN demonstrates a 57%–58.4% improvement in training efficiency. The extended model generalizes well across varying Richardson numbers, highlighting its effectiveness for ill-posed mixed convection problems and its promise in advancing data-physics fusion in computational fluid dynamics.