Wave-Former: Lag removing univariate long time series forecasting transformer for ocean waves

Abstract

Long-Sequence Time Series Forecasting (LSTSF) of ocean waves using univariate modelling has always been a challenging task in the field of oceanography as it demands a high prediction capacity model capable to capture precise long-range dependency between input and output variables. Inherently, it exhibits the problem of “time lag or phase shift” in predictions which is due to high autocorrelation in between time dependent sequential values. Very few researchers had tried to remove this “phase shift” problem in the univariate modelling including the author of present work wherein preprocessing of time series data was done by different methods. Many failed in gaining high prediction accuracy at longer forecasting intervals. Overcoming these limitations, present work aims for LSTSF of ocean waves ranging from 24 to 144 hours (hrs) at the three locations of Gulf of Mexico using “WaveFormer” architecture based on the Informer. Probabilistic self-attention mechanism has proved to be efficient to remove the “time lag or phase shift” in ocean waves as well as in predicting the waves at large time intervals (144 hrs). Low Root Mean Squared Errors (RMSEs) (0.045–0.100) and high correlation coefficients (0.90–0.99), low values of test loss (0.002–0.012) of all the developed models demonstrated the competency of WaveFormer.