Neural Operator Prediction of the Stress Distribution within Coastal Cliffs due to Ocean Wave Action

Ocean wave action is one of the primary drivers of coastal cliff erosion. Due to global warming, ocean waves have become stronger, causing worsening erosion. To protect coastal cliffs, we need an effective tool for predicting where and how erosion will occur. To this end, our research aimed to create a set of Fourier Neural Operators that, given an arbitrarily shaped coastal cliff, can accurately predict either the stress distribution that would result from ocean wave action or the ocean wave shape. To generate our training and testing datasets, we ran 1400 simulations of an ocean wave crashing against coastal cliffs. The ocean wave was simulated using the particle in cell method and the velocity stress wave was solved using the finite difference method. In the end, we created four ensembles of neural operators: three that can predict the stress distribution at three different time steps and one that can predict the ocean wave shape at one particular time step. Using scaled outputs, the neural operators had errors of 9E-05, with the error continuing to decrease with more training epochs. Additionally, plots of the validation tests showed very promising results. Because a neural operator acts as a solution operator, it will be magnitudes faster than any numerical method, thereby providing researchers with a time-saving tool. Indeed, we found that our neural operators provided the solution 571 to 857 times faster than the aforementioned numerical methods used to create the dataset.