Neural operator
Definition
A neural operator is a neural network that learns a mapping between functions rather than between fixed-size vectors. In simulation, it learns the solution operator of a family of partial differential equations: given an input field, such as a boundary condition or a material property, it predicts the solution field, and the same trained model works across different discretizations.
Example
A Fourier neural operator trained on flow solutions at one grid resolution can be evaluated at a finer resolution without retraining, because its parameters don't depend on the grid. The Fourier neural operator and DeepONet are the two best-known families.
Sources
- Kovachki et al., "Neural Operator: Learning Maps Between Function Spaces," JMLR, 2023, arxiv.org/abs/2108.08481
- Li et al., "Fourier Neural Operator for Parametric Partial Differential Equations," 2020, arxiv.org/abs/2010.08895