Survey: Adaptive Physics-informed Neural Networks

Physics-informed neural networks (PINNs) present a promising solution for solving partial differential equations (PDEs) using neural networks, especially in data-scarce scenarios due to their unsupervised learning abilities. However, a key limitation is the need for re-optimization with every change in PDE parameters, similar to the constraints in traditional numerical methods, which limits the broader use of PINNs. This survey explores research addressing this limitation through transfer learning and meta-learning. These methods can potentially improve PINNs’ training efficiency, enabling quicker adaptation to new PDEs with fewer data and computational demands. Instead of relying on extensive data to build general models, typical for existing foundation model approaches, efficient adaptation in PINNs focuses on smaller information domains that quickly adjust to similar problems by leveraging previously learned knowledge. By synthesizing insights from these advanced learning techniques, this survey identifies strategies to facilitate the broader adoption of PINNs across scientific and engineering fields.