Representation equivalent Neural Operators

In operator learning, it has been observed that proposed models may not behave as operators when implemented on a computer, questioning the very essence of what operator learning should be. We contend that some form of continuous-discrete equivalence is necessary for an architecture to genuinely learn the underlying operator, rather than just discretizations of it. Employing frames, we introduce the framework of Representation equivalent Neural Operator (ReNO) to ensure operations at the continuous and discrete level are equivalent.
Joint work with Francesca Bartolucci (TU Delft), Emmanuel de Bézenac (ETH Zurich), Bogdan Raoni (ETH Zurich), Roberto Molinaro (ETH Zurich), Siddhartha Mishra (ETH Zurich).