Physics-informed neural networks (PINNs) suffer from prolonged convergence plateaus due to random initialization, which severely limits their practical applications. To address this challenge, this study proposes a novel two-stage framework named Data Migration PINNs (DM-PINNs), which decouples the training process into data migration and physics enhancement stages. This approach effectively leverages prior knowledge from cost-effective data to accelerate training and prevents competition between the data-driven and physics-based loss functions. In the data migration phase, an approximate flowfield is produced using a surrogate model constructed from historical data. The network is then pretrained based on this data set, thereby establishing an initialization derived from prior knowledge. During the physics enhancement stage, the Navier–Stokes equation residuals and boundary condition constraints are employed to improve physical fidelity. Validated on airfoil flow prediction, DM-PINNs eliminate the stagnation period and accelerate convergence, with these improvements becoming increasingly significant at higher Reynolds numbers. At Formula: see text, a convergence acceleration of approximately 47% is observed. Furthermore, the prediction of the proposed model exhibits strong agreement with high-fidelity benchmarks, with errors primarily concentrated in flow regions characterized by high gradients and complex physical phenomena.
Wang et al. (Mon,) studied this question.