Data-efficient surrogate modeling using meta-learning and physics-informed deep learning approaches

This paper proposes physics-informed meta-learning-based surrogate modeling (PI-MLSM), a novel approach that combines meta-learning and physics-informed deep learning to train surrogate models with limited labeled data. PI-MLSM consists of two stages: meta-learning and physics-informed task adaptation. The proposed approach is demonstrated to outperform other methods in four numerical examples while reducing errors in prediction and reliability analysis, exhibiting robustness, and requiring less labeled data during optimization. Moreover, compared to other approaches, the proposed approach exhibits better performance in solving out-of-distribution tasks. Although this paper acknowledges certain limitations and challenges, such as the subjective nature of physical information, it highlights the key contributions of PI-MLSM, including its effectiveness in solving a wide range of tasks and its ability in handling situations wherein physical laws are not explicitly known. Overall, PI-MLSM demonstrates potential as a powerful and versatile approach for surrogate modeling. •A proposed approach uses meta-learning and PIDL to train surrogates with small data.•A model-agnostic meta-learning model is introduced to learn surrogate model weights.•A PIDL approach is introduced to adapt to target tasks with meta-learned weights.•Our approach outperformed other methods in numerical examples given limited data.•Proposed approach showed robustness in solving out-of-distribution tasks.