Compact FFT-based machine-learning model for efficient short-range forecasting of unidirectional waves

This paper presents a data-driven method using neural networks to forecast unidirectional irregular waves. The approach predicts downstream wave elevation based on a single upstream probe measurement. Operating in the frequency domain, the model applies a Sliding Fast Fourier Transform (SFFT) to decompose the signal into the temporal evolution of its modal components. A Softmax kernel serves as a temporal attention gate to adaptively weight past measurements of the decomposed modes (amplitude and phase). With fewer than one hundred trainable parameters, the model is highly interpretable, computationally efficient, and fast during inference. Validation against experimental data demonstrates strong agreement, achieving surface similarity parameter (SSP) errors on average 0.15 for short-range forecasts (up to 1.5 wavelengths and 2 wave periods). Furthermore, implementing an overlap-and-add method enables smooth, continuous time-series prediction and further improves accuracy, confirming the potential of this machine learning approach as an efficient and reliable solution for marine and coastal applications.