Neural Network Prediction of Ocean Wave Behavior Using Frequency Domain Mapping

As ocean levels rise, and global weather events become more extreme, it is more important than ever to understand, visualize, and predict ocean wave behavior. Such predictions, especially if done with low latency, are an important component of emergency preparation. For example, the ability to predict where a tsunami will hit is key to safeguarding coastal communities, ships, fishermen, and offshore platforms. In recent years, key advances have been made in the application of neural networks toward weather related predictions. One neural network architecture, the Fourier Neural Operator (FNO), has shown great promise in image to image mapping where the images represent the solution space of a physical system. In the current research, we use an FNO to predict ocean wave behavior in near real-time. We generated FNO training data by solving by solving the shallow water equations using traditional numerical methods. Although this method is a 2.5D solution to a 3D problem, we believe it is an important initial step to showing whether a more complex and intensive approach is warranted. Using any arbitrarily-shaped ocean basin topography as the input, we tasked the FNO with predicting the resulting wave height for a pre-determined time step. Using only 1,050 training points of
$128\times 128$
resolution, the FNO performed well on validation inputs of resolution
$1024\times 1024$
. When tasked with predicting the tsunami wave front on just a single ocean basin topography, the FNO learned exceptionally well, with error in the wave height on the order of 3.88E-7.