A Physics-informed machine learning model for time-dependent wave runup prediction

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.