A discretization-invariant extension and analysis of some deep operator networks

Understand

We present a generalized version of the discretization-invariant neural operator and prove that the network is a universal approximation in the operator sense.

• Moreover, by incorporating additional terms in the architecture, we establish a connection between this discretization-invariant neural operator network and those discussed before.
• The discretization-invariance property of the operator network implies that different input functions can be sampled using various sensor locations within the same training and testing phases.
• Additionally, since the network learns a ``basis'' for the input and output function spaces, our approach enables the evaluation of input functions on different discretizations.