  A large class of inverse problems for PDEs are only well-defined as mappings
from operators to functions. Existing operator learning frameworks map
functions to functions and need to be modified to learn inverse maps from data.
We propose a novel architecture termed Neural Inverse Operators (NIOs) to solve
these PDE inverse problems. Motivated by the underlying mathematical structure,
NIO is based on a suitable composition of DeepONets and FNOs to approximate
mappings from operators to functions. A variety of experiments are presented to
demonstrate that NIOs significantly outperform baselines and solve PDE inverse
problems robustly, accurately and are several orders of magnitude faster than
existing direct and PDE-constrained optimization methods.
