Here I note on the pyTorch implementation of different types of neural operators:

  • Fourier Neural Operator (FNO)
  • Spherical FNO (SFNO)
  • Markov Neural Operator (MNO)
  • Geometry-Informed Neural Operator (GINO)
  • Physics-Informed Neural Operator (PINO)

Fourier Neural Operator (FNO)

The now classical work of Fourier Neural Operator has been quite influential in the class of work known as neural partial differential equations (Neural PDEs).

Spherical Neural Operator (SFNO)

The spherical neurla operator is a particular adaptation of the FNO to a spherical domain.

Markov Neural Operator (MNO)

The Markov Neural Operator is a particular adaptation of the FNO to dissipative dynamical systems.

Geometry-Informed Neural Operator (GINO)

GINO attempts to solve the problem of FNO only applicable to regular grids.

Physics-Informed Neural Operator (PINO)

PINO attempts to combine the two paradigms of sciML: physics-informed neural network and operator learning.