  Wave runup is a critical factor affecting coastal flooding, shoreline
changes, and damage to coastal structures. Climate change is also expected to
amplify wave runup's impact on coastal areas. Therefore, fast and accurate wave
runup estimation is essential for effective coastal engineering design and
management. However, predicting the time-dependent wave runup is challenging
due to the intrinsic nonlinearities and non-stationarity of the process, even
with the use of the most advanced machine learning techniques. In this study, a
physics-informed machine learning-based approach is proposed to efficiently and
accurately simulate time-series wave runup. The methodology combines the
computational efficiency of the Surfbeat (XBSB) mode with the accuracy of the
nonhydrostatic (XBNH) mode of the XBeach model. Specifically, a conditional
generative adversarial network (cGAN) is used to map the image representation
of wave runup from XBSB to the corresponding image from XBNH. These images are
generated by first converting wave runup signals into time-frequency scalograms
and then transforming them into image representations. The cGAN model achieves
improved performance in image-to-image mapping tasks by incorporating
physics-based knowledge from XBSB. After training the model, the high-fidelity
XBNH-based scalograms can be predicted, which are then employed to reconstruct
the time-series wave runup using the inverse wavelet transform. The simulation
results underscore the efficiency and robustness of the proposed model in
predicting wave runup, suggesting its potential value for applications in risk
assessment and management.
