Prediction of nonlinear wave statistics using machine learning models trained on wave-resolving nearshore hydrodynamics models

Abstract

The modeling of nearshore hydrodynamics demands extraordinary computational power to resolve vastly different scales and processes of interest. To remain tractable, models make trade-offs in what to resolve, at what scale to model, and which processes are parameterized, estimated, or neglected. Wave-averaging represents one such trade-off, whereby variation on the temporal order of a wave period is neglected to instead model properties of the wave field at large. This contrasts with the computationally more demanding wave-resolving models, whereby the time-varying motion of waves within individual wave periods is captured. ☐ Due to their time-averaged nature, wave-averaged models cannot inherently model nonlinear evolution in wave shape in the same way that wave-resolving models can. Such changes are often characterized by the higher-order statistics of skewness and asymmetry. Such higher-order quantities are crucial to understanding complex, coupled processes, such as morphodynamics and sediment transport. However, the computational cost of wave-resolving Boussinesq models makes their application to long time scales and complex coupling formulations impractical for many applications, such as morphodynamics. Consequently, it is difficult to leverage the power of many nonlinear wave models at longer time scales. ☐ The development of scalable machine learning (ML) algorithm has provided new opportunities to bridge scale gaps and couple models. In this vein, the wave-resolving Boussinesq model FUNWAVE-TVD was first validated on experimental data and run upwards of 20,000 times on different representative beach profiles and wave spectra from Duck, North Carolina to generate a corpus of training data to model skewness and asymmetry in the cross-shore. ☐ Principal component analysis (PCA) was used to characterize the variability of the input and output spaces, identify outliers in the dataset, and fit a baseline regression model to capture simple linear dependencies in a low-rank space. This analysis also reveals the hidden relationships between wave skewness and offshore wave spectral as well as wave asymmetry and bathymetry, providing insight into more effective nonlinear ML modeling. Additional machine learning models exploiting nonlinear mappings to low-dimensional latent spaces via kernels were also applied. An encoder-decoder architecture based on a convolutional neural network (CNN) was implemented to capture spatial patterns in the bathymetry and sequential structure in the spectra. Furthermore, decision-tree-based models, including random forest regressors and XGBoost, were fit due to their effectiveness in modeling highly nonlinear relationships. All models demonstrated robustness to overfitting with appropriate hyperparameter tuning, suggesting that low-rank representations and machine-learning-based surrogate models can effectively replicate complex nearshore statistics derived from wave-resolving models in a computationally efficient manner.