Meta-PINNs: Meta-Learning Enhanced Physics-Informed Machine Learning Framework for Turbomachinery Flow Predictions under Varying Operation Conditions

Abstract

Coupling physics with machine learning models has shown great potential for solving fluid dynamics problems governed by partial differential equations. However, conventional methods, such as physics-informed neural networks, often suffer from slow convergence, unstable training, and limited generalization across different flow conditions. To overcome these challenges, this study proposes a novel meta-learning en- hanced physics-informed neural networks (Meta-PINNs) framework, which integrates a meta-optimization strategy into the training process. The approach allows the model to automatically adapt its learning process to varying physical regimes, thereby substantially improving both training efficiency and predictive robustness. The proposed Meta-PINNs model is evaluated on two representative flow problems: (1) unsteady flow around a circular cylinder at multiple inlet Reynolds numbers, and (2) steady turbulent flow within a compressor cascade passage at various angles of attack. In both cases, the extrapolation performance of the developed framework is comprehensively tested by predicting the flow fields at Reynolds numbers and angles of attack that are not included in the training set. The results demonstrate that Meta-PINNs achieve a 1-2 order-of-magnitude improvement in accuracy over vanilla physics-informed neural networks and standard neural networks, while reducing computational cost by up to 95.7 % and 92.1 %, respectively. It successfully captures the sequential patterns of key flow features such as pressure and velocity distributions under unseen conditions. Thus, the findings confirm that the Meta-PINNs framework offers a notable improvement in convergence and generalization over existing machine learning approaches, providing a promising pathway toward smart simulations of complex turbomachinery flows.