Phase-resolved wave prediction with linear wave theory and physics-informed neural networks

Abstract

Deterministic wave elevation prediction is crucial for improving the power generation efficiency of offshore energy structures (OESs). Although phase-resolved wave models may predict deterministic wave information, a comprehensive understanding of wave theory and mathematics is necessary to guarantee their accuracy. Inspired by the capability of physics-informed neural networks (PINNs) in solving physical equations, we propose an irregular long-crested wave prediction model named LWT-PINN that combines the linear wave theory (LWT) with PINNs. To the best of our knowledge, this is the first time that PINNs are used to predict waves. Five sets of wave elevation time series with steepness ranging from 0.0174 to 0.0349 are generated in a wave basin to optimize and evaluate the LWT-PINN. The computing time for LWT-PINN is 0.13 s, close to real-time. When predicting downstream wave elevation, the LWT-PINN significantly outperforms the linear wave prediction (LWP) model in terms of accuracy and prediction length. Specifically, the LWT-PINN achieves satisfactory accuracy with only 100 s upstream wave elevation, whereas the LWP requires 175 s; LWT-PINN’s high-precision prediction duration is 13.7 s, which is 2.5 times longer than that of LWP (5.5 s). Moreover, LWT-PINN can provide wave autoregressive predictions of around 5 s without the aid of statistical methods, which offers a new direction for developing wave autoregressive prediction methods. The excellent performance of the proposed model can substantially assist the stable operation of OESs.