Neural Operator: Is data all you need to model the world? An insight into the paradigm of data-driven scientific ML

One of the earliest systematic surveys of the neural-operator paradigm. It benchmarks classical ML PDE approaches, then maps the operator architecture family (DeepONet, GNO, FNO, Geo-FNO, PINO, AFNO, GNOT, IPOT), and surveys diffusion-based operator frameworks.

Reading order: Section II for ML-on-PDE background → Section III for operator-family → Section V for open problems on zero-shot generalization across PDE parameterizations and geometries.