  The use of neural operators in a digital twin model of an offshore floating
structure can provide a paradigm shift in structural response prediction and
health monitoring, providing valuable information for real-time control. In
this work, the performance of three neural operators is evaluated, namely, deep
operator network (DeepONet), Fourier neural operator (FNO), and Wavelet neural
operator (WNO). We investigate the effectiveness of the operators to accurately
capture the responses of a floating structure under six different sea state
codes $(3-8)$ based on the wave characteristics described by the World
Meteorological Organization (WMO). The results demonstrate that these
high-precision neural operators can deliver structural responses more
efficiently, up to two orders of magnitude faster than a dynamic analysis using
conventional numerical solvers. Additionally, compared to gated recurrent units
(GRUs), a commonly used recurrent neural network for time-series estimation,
neural operators are both more accurate and efficient, especially in situations
with limited data availability. To further enhance the accuracy, novel
extensions, such as wavelet-DeepONet and self-adaptive WNO, are proposed. Taken
together, our study shows that FNO outperforms all other operators for
approximating the mapping of one input functional space to the output space as
well as for responses that have small bandwidth of the frequency spectrum,
whereas for learning the mapping of multiple functions in the input space to
the output space as well as for capturing responses within a large frequency
spectrum, DeepONet with historical states provides the highest accuracy.
