Engineering practice has historically relied on models grounded in ordinary and partial differential equations (PDEs) to relate system inputs, such as forces, fluxes, or heat sources, to observable outputs, such as displacement, concentration, or temperature. These physics-based models are interpretable and generalizable, but they require deep domain knowledge and significant computational resources. Scientific machine learning (SciML), and in particular operator learning, offers an alternative strategy to predictive modeling: neural networks trained directly on data to approximate the input-output relationship traditionally furnished by PDEs. These learned operators can be highly accurate, computationally efficient, and do not require mechanistic insight into the system under study, but they lack interpretability and fail to make meaningful predictions when queried outside the training data.

In this paper, we argue that learned operators constitute a novel kind of scientific model, and are under-theorized from a philosophical perspective. Unlike traditional phenomenological laws, they attempt to entirely replace governing PDEs with high-dimensional data-driven mappings. Drawing on work in the philosophy of scientific explanation, laws, and models, we examine how surrogate models fit---or fail to fit---within existing philosophical frameworks. We argue that their limited scope, opacity, vulnerability to adversarial attack, and neglect of unobservable entities distinguish them from theory-based models in epistemically significant ways. Additionally, we suggest that new frameworks for verification and validation are required if learned operators are to be safely integrated into scientific and engineering practice.