From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing

The review distills practical wisdom: which architecture fits which PDE family, how to size training data, residual-based error correction, and multi-level training for accuracy control.

Recommended path: skim the architecture comparison, run the published Jupyter notebooks (CEADpx/neural_operators), then adapt the Bayesian-inversion recipe to your own inverse problem.

Companion repo: https://github.com/CEADpx/neural_operators/ (tag survey25_v1)