Rapid phase-resolved prediction of nonlinear dispersive waves using machine learning

The phase-resolved prediction of ocean waves suffers from two major challenges that have so far hindered solutions in real time or faster: (i) The reconstruction of the nonlinear and dispersive waves: how to calculate the state of the wavefield from measurable wave amplitude data, and (ii) Rapid solution: how to integrate equations in a timely manner. Here, we overcome these challenges at once through an advanced machine learning technique based on spatiotemporal patches of the time history of surface wave elevation data in the domain. The proposed time-series analysis uses a new concept of convolution that instead of constructing kernels from filters, implements random patches of spatiotemporal data as the input to predict the next patch. We demonstrate that the proposed methodology can accurately make predictions for ocean surface gravity waves more than two orders of magnitude faster than numerically solving governing equations.