  Operator learning frameworks, because of their ability to learn nonlinear
maps between two infinite dimensional functional spaces and utilization of
neural networks in doing so, have recently emerged as one of the more pertinent
areas in the field of applied machine learning. Although these frameworks are
extremely capable when it comes to modeling complex phenomena, they require an
extensive amount of data for successful training which is often not available
or is too expensive. However, this issue can be alleviated with the use of
multi-fidelity learning, where a model is trained by making use of a large
amount of inexpensive low-fidelity data along with a small amount of expensive
high-fidelity data. To this end, we develop a new framework based on the
wavelet neural operator which is capable of learning from a multi-fidelity
dataset. The developed model's excellent learning capabilities are demonstrated
by solving different problems which require effective correlation learning
between the two fidelities for surrogate construction. Furthermore, we also
assess the application of the developed framework for uncertainty
quantification. The results obtained from this work illustrate the excellent
performance of the proposed framework.
