Strategies for Pretraining Neural Operators
This work addresses the limited understanding of pretraining effects in neural operators for PDE modeling, providing insights for future method development, though it is incremental as it focuses on comparison rather than introducing new techniques.
The study compared various pretraining methods for neural operators on PDE modeling to understand their scaling and generalization behavior, finding that transfer learning or physics-based strategies work best and performance improves with data augmentations.
Pretraining for partial differential equation (PDE) modeling has recently shown promise in scaling neural operators across datasets to improve generalizability and performance. Despite these advances, our understanding of how pretraining affects neural operators is still limited; studies generally propose tailored architectures and datasets that make it challenging to compare or examine different pretraining frameworks. To address this, we compare various pretraining methods without optimizing architecture choices to characterize pretraining dynamics on different models and datasets as well as to understand its scaling and generalization behavior. We find that pretraining is highly dependent on model and dataset choices, but in general transfer learning or physics-based pretraining strategies work best. In addition, pretraining performance can be further improved by using data augmentations. Lastly, pretraining can be additionally beneficial when fine-tuning in scarce data regimes or when generalizing to downstream data similar to the pretraining distribution. Through providing insights into pretraining neural operators for physics prediction, we hope to motivate future work in developing and evaluating pretraining methods for PDEs.