  Operator learning is an emerging area of machine learning which aims to learn
mappings between infinite dimensional function spaces. Here we uncover a
connection between operator learning architectures and conditioned neural
fields from computer vision, providing a unified perspective for examining
differences between popular operator learning models. We find that many
commonly used operator learning models can be viewed as neural fields with
conditioning mechanisms restricted to point-wise and/or global information.
Motivated by this, we propose the Continuous Vision Transformer (CViT), a novel
neural operator architecture that employs a vision transformer encoder and uses
cross-attention to modulate a base field constructed with a trainable
grid-based positional encoding of query coordinates. Despite its simplicity,
CViT achieves state-of-the-art results across challenging benchmarks in climate
modeling and fluid dynamics. Our contributions can be viewed as a first step
towards adapting advanced computer vision architectures for building more
flexible and accurate machine learning models in physical sciences.
