This paper presents a novel deep learning framework for estimating multivariate joint extremes of metocean variables, based on the Semi-Parametric Angular-Radial (SPAR) model. When considered in polar coordinates, the problem of modelling multivariate extremes is transformed to one of modelling an angular density, and the tail of a univariate radial variable conditioned on angle. In the SPAR approach, the tail of the radial variable is modelled using a generalised Pareto (GP) distribution, providing a natural extension of univariate extreme value theory to the multivariate setting. In this work, we show how the method can be applied in higher dimensions, using a case study for five metocean variables: wind speed, wind direction, wave height, wave period and wave direction. The angular variable is modelled empirically, while the parameters of the GP model are approximated using fully-connected deep neural networks. Our data-driven approach provides great flexibility in the dependence structures that can be represented, together with computationally efficient routines for training the model. Furthermore, the application of the method requires fewer assumptions about the underlying distribution(s) compared to existing approaches, and an asymptotically justified means for extrapolating outside the range of observations. Using various diagnostic plots, we show that the fitted models provide a good description of the joint extremes of the metocean variables considered.

翻译：本文提出了一种基于半参数角径向（SPAR）模型的新型深度学习框架，用于估计海洋气象变量的多元联合极端值。在极坐标系下考虑时，多元极值建模问题转化为角密度建模问题，以及以角度为条件的单变量径向变量尾部分布建模问题。在SPAR方法中，径向变量的尾部采用广义帕累托（GP）分布进行建模，这为单变量极值理论向多元场景的扩展提供了自然途径。本研究通过包含风速、风向、波高、波周期和波方向五个海洋气象变量的案例，展示了该方法在高维场景中的应用。角变量采用经验方法建模，而GP模型的参数则通过全连接深度神经网络进行近似估计。我们的数据驱动方法在可表征的依赖结构方面具有高度灵活性，同时提供了高效的计算流程用于模型训练。此外，与现有方法相比，本方法对基础分布的假设要求更少，并提供了在观测范围外进行渐近合理性外推的手段。通过多种诊断图表明，所拟合的模型能很好地描述所研究海洋气象变量的联合极端特征。