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.
翻译:代用模型往往用来取代成本高昂的复杂沿海法规,以节省大量计算费用。在许多此类模型中,水文气象强迫条件(投入)或洪涝事件(产出)都方便地以星标表示参数,忽视投入实际上是时间序列,洪水在空间上向内陆传播。两种事实对于复杂沿海系统的洪水预测都至关重要。我们的目的是建立一个代用模型,记录时间变化的投入,并提供空间变化的内陆洪水信息。我们引入了多输出高斯进程模型,该模型以功能投入和空间位置相关的可分离内核为基础。高效实施考虑到高压结构的计算或稀变近似。在几个实验中,我们展示了模型在学习地图和推断未观测的地图方面的多功能性。我们的目的是建立一个代用模型,以数字方式显示随着学习地图数量的增加而预测的汇合情况。我们在沿海洪水预测应用中评估了我们的框架。在计算与短期预测要求高度相容的时段内,以小错误值获得预测值。高效的执行考虑到高层次的计算方法或稀有差异的差差差差差差差差差差差值。在水文预测中,我们通过预测系统来得出了需要的时的时的时段的时段,以预测。我们为预测。我们所需要的时,我们为时的时的时的时的时序路路流测测测测。