Abstract
This paper presents our winning entry for the EVA 2019 data competition, the aim of which is to predict Red Sea surface temperature extremes over space and time. To achieve this, we used a stochastic partial differential equation (Poisson equation) based method, improved through a regularization to penalize large magnitudes of solutions. This approach is shown to be successful according to the competition’s evaluation criterion, i.e. a threshold-weighted continuous ranked probability score. Our stochastic Poisson equation and its boundary conditions resolve the data’s non-stationarity naturally and effectively. Meanwhile, our numerical method is computationally efficient at dealing with the data’s high dimensionality, without any parameter estimation. It demonstrates the usefulness of stochastic differential equations on spatio-temporal predictions, including the extremes of the process.
Highlights
The aim of EVA 2019 data competition is to predict spatio-temporal extremes of Red Sea surface temperature (Huser 2020)
Experimental results show that it is effective and efficient to use the regularized stochastic Poisson equation to fill in the missing data in this problem
For some points in the gray region, they can be sampled as cross-validation points if their spatio-temporal neighborhood N (·, ·) is completely available in the original training set, which are shown as black dots in the right of Fig. 4
Summary
The aim of EVA 2019 data competition is to predict spatio-temporal extremes of Red Sea surface temperature (Huser 2020). We formulate the missing value prediction problem as a Poisson equation based model. The stochastic components (i.e. the Laplace fields) in our SPDEs (stochastic partial differential equations) are sampled from the observed data, assuming temporal stationarity, which allows bypassing explicit estimation of parameters defining a stochastic model. Experimental results show that it is effective and efficient to use the regularized stochastic Poisson equation to fill in the missing data in this problem.
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