Neural operator models offer a path toward modeling physical systems at low computational cost by learning mappings between function spaces. However, as mesh sizes and model parameter counts scale up, standard operator architectures face steep computational bottlenecks.

In this presentation, I will motivate neural operator design directly from a test-time learning perspective. I will demonstrate how attention-based operators and sub-quadratic mechanisms that scale favorably with input resolution can be derived from this unified principle. Finally, I will present architecture designs that are performant and parameter-efficient, often competing with or surpassing much larger foundation models. Together, these results offer a principled design language for efficient and stable scientific surrogates.