  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 is 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.
