Neural-network-based super-resolution on unstructured meshes of coastal spectral wave computations

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High-resolution wave forecasts are of critical importance for coastal safety, hazard prevention, and energy transition. Examples that benefit from detailed information of coastal sea states range from the adaptation of coastal protection to beach goer and marine safety and even include the growing market of marine renewable energy. While regional and global wave forecasts exist, local high-resolution details are often not accessible due to the associated computational cost.In our work we use a neural network to apply a so-called super-resolution approach that can turn wave forecasts computed over coarse grids into substantially higher resolution at very low computation cost and with only little loss of overall quality. The idea is to train the neural network with pairs of coarse and fine-grid computations, so that later on wave computations over coarse grids can be converted into a higher resolution. While the amount of saved computation time varies with the level of resolution between coarse and fine grid, the super-resolution approach can be more than 50-times faster than a direct high-resolution computation and still provide good accuracy.Here we will present a case study on a 44-year hindcast of the French Basque coast, with which we trained and tested multiple networks. We will comment on the dependency of model performance on the amount of training data and the difficulties of an unstructured grid, compared to a structured one. More specifically, structured grids can be handled as regular images, which makes the adaptation of classical and powerful convolutional neural networks to the problem relatively easy. The application to irregular grids, however, is not trivial and requires different approaches like graph neural networks or multi-layer perceptrons.  Lastly, we will compare the performance of a surrogate model, that is, a neural network that simply replaces completely a spectral wave model like SWAN, with our super-resolution approach, that uses coarse wave model computations as an input. We argue that both approaches are complementary and have their advantages and disadvantages in specific settings.