Applications of the Fourier neural operator in a regional ocean modeling and prediction

In this paper, we apply the Fourier neural operator (FNO) paradigm to ocean circulation and prediction problems. We aim to show that the complicated non-linear dynamics of an ocean circulation can be captured by a flexible, efficient, and expressive structure of the FNO networks. The machine learning model (FNO3D and the recurrent FNO2D networks) trained by simulated data as well as real data takes spatiotemporal input and predicts future ocean states (sea surface current and sea surface height). For this, the double gyre ocean circulation model driven by stochastic wind stress is considered to represent an ideal ocean circulation. In order to generate the training and test data that exhibits rich spatiotemporal variability, the initial states are perturbed by Gaussian random fields. Experimental results confirm that the trained models yield satisfactory prediction accuracy for both types of FNO models in this case. Second, as the training set, we used the HYCOM reanalysis data in a regional ocean. FNO2D experiments demonstrated that the 5-day input to 5-day prediction yields the averaged root mean square errors (RMSEs) of 5.0 cm/s, 6.7 cm/s, 7.9 cm/s, 8.9 cm/s, and 9.4 cm/s in surface current, calculated consecutively for each day, in a regional ocean circulation of the East/Japan Sea. Similarly, the RMSEs for sea surface height were 2.3 cm, 3.5 cm, 4.2 cm, 4.6 cm, and 4.9 cm, for each day. We also trained the model with 15-day input and 10-day prediction, resulting in comparable performance. Extensive numerical tests show that, once learned, the resolution-free FNO model instantly forecasts the ocean states and can be used as an alternative fast solver in various inference algorithms.