These methods can be broadly categorized into two types: function learning and operator learning approaches. In function learning, the goal is to directly learn the solution.

Fourier Neural Operators (FNOs) have shown promise for solving partial differential equations (PDEs).

Here, we present novel adaptations for convolutional neural networks to demonstrate that they are indeed able to process functions as inputs and outputs.

We consider the problem of discretization of neural operators between Hilbert spaces in a general framework including skip connections. We focus on bijec-tive neural operators through the lens of diffeomorphisms in infinite dimensions.

This research offers a fresh take on neural operators with a framework Representation equivalent Neural Operators (ReNO) designed to address these issues.

It is common that these data themselves have inherently complicated 3D geometric structures.