Machine Learning Emulation of High Resolution Inundation Maps

Estimating coastal tsunami impact for early-warning or long-term hazard analysis requires the calculation of inundation metrics such as flow-depth or momentum flux. Both applications require the simulation of large numbers of scenarios to capture both the aleatory variability and the epistemic tsunami uncertainty. A computationally demanding step in simulating inundation is solving the nonlinear shallow water (NLSW) equations on meshes with sufficiently high resolution to represent the local elevation accurately enough to capture the physics governing the flow. This computational expense is particularly challenging in the context of Tsunami Early Warning where strict time constraints apply. A Machine Learning (ML) model that predicts inundation maps from offshore simulation results with acceptable accuracy, trained on an acceptably small training set of full simulations, could replace the computationally expensive NLSW part of the simulations for vast numbers of scenarios and predict inundation rapidly and with reduced computational demands. We consider the application of an encoder-decoder based neural network to predict high-resolution inundation maps based only on more cheaply calculated simulated time-series at a limited number of offshore locations. The network needs to be trained using input offshore time-series and the corresponding inundation maps from previously calculated full simulations. We develop and evaluate the ML model on a comprehensive set of inundation simulations for the coast of eastern Sicily for tens of thousands of subduction earthquake sources in the Mediterranean Sea. We find good performance for this case study even using relatively small training sets (order of hundreds) provided that appropriate choices are made in the specification of model parameters, the specification of the loss function, and the selection of training events. The uncertainty in the prediction for any given location decreases with the number of training events that inundate that location, with a good range of flow depths needed for accurate predictions. This means that care is needed to ensure that rarer high-inundation scenarios are well-represented in the training sets. The importance of applying regularization techniques increases as the size of the training sets decreases. The computational gain of the proposed methodology depends on the number of complete simulations needed to train the neural network, ranging between 164 and 4196 scenarios in this study. The cost of training the network is small in comparison with the cost of the numerical simulations and, for an ensemble of around 28000 scenarios, this represents a 6 to 170-fold reduction in computing costs.