Neural Operator Simulation of Turbulent Multiphase Flow with Applications in Ocean Wave Modeling

Global warming has increased ocean wave heights and the frequency of extreme wave events. As a result, ocean waves have contributed to more coastal erosion, flooding, and fatigue damage of ocean-based structures. Researchers interested in understanding the effects of ocean waves must rely on slow numerical methods such as particle-in-cell (PIC), which can take hours. Therefore, researchers have good occasion to find a faster alternative for modeling ocean waves. Here, we present a Fourier Neural Operator (FNO) for predicting ocean wave behavior on grids of arbitrary geometry. An FNO is designed to map an input image to an output image in infinite dimensions. This allows the FNO to act as a solution operator, which decreases computational complexity. To create data for our FNO, we used the PIC method to create 290 simulations of an ocean wave crashing against a random obstruction, i.e., some arbitrary geometry. Each simulation modeled 38,000 water particles for 600 time steps, which required 30 minutes. From these simulations, we created training and testing datasets of 274 and 16 image pairs, respectively. We trained the FNO for 75 epochs, which took 900 seconds. After training, we validated the FNO against our 16 test points. At a resolution of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$256 \times 256$</tex>, our FNO had an inference time of only 0.073 second. Our FNO results were good, especially since only 274 training points were used. Using our approach, FNOs can be designed to predict levee overtopping, flooding, blast waves, and the effect of water drops over wildfires.