Multioutput Gaussian Processes with Functional Data: A Study on Coastal Flood Hazard Assessment

TL;DR

This paper develops a multioutput Gaussian process model that incorporates time series inputs and spatial information to improve coastal flood hazard prediction, offering fast and accurate forecasts for early-warning systems.

Contribution

The paper introduces a novel multioutput Gaussian process model with a separable kernel that accounts for functional inputs and spatial locations, enhancing flood prediction accuracy and efficiency.

Findings

Model achieves low prediction errors in coastal flood scenarios.

Predictions are generated within minutes, suitable for real-time forecasting.

The approach outperforms traditional models in accuracy and computational speed.

Abstract

Surrogate models are often used to replace costly-to-evaluate complex coastal codes to achieve substantial computational savings. In many of those models, the hydrometeorological forcing conditions (inputs) or flood events (outputs) are conveniently parameterized by scalar representations, neglecting that the inputs are actually time series and that floods propagate spatially inland. Both facts are crucial in flood prediction for complex coastal systems. Our aim is to establish a surrogate model that accounts for time-varying inputs and provides information on spatially varying inland flooding. We introduce a multioutput Gaussian process model based on a separable kernel that correlates both functional inputs and spatial locations. Efficient implementations consider tensor-structured computations or sparse-variational approximations. In several experiments, we demonstrate the versatility of the model for both learning maps and inferring unobserved maps, numerically showing the convergence of predictions as the number of learning maps increases. We assess our framework in a coastal flood prediction application. Predictions are obtained with small error values within computation time highly compatible with short-term forecast requirements (on the order of minutes compared to the days required by hydrodynamic simulators). We conclude that our framework is a promising approach for forecast and early-warning systems.