发表机构
Department of Mathematical Sciences, Ball State University; Statistics Discipline, Division of Science and Mathematics, University of Minnesota-Morris（数学科学系，巴尔的摩州立大学; 统计学学科，明尼苏达-莫里斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究针对多变量时空预测中不确定性难处理的问题，提出TSCoNet模型，它是结合高斯Copula的两阶段卷积循环模型，能同时准确预测多个变量并量化不确定性，为多变量时空数据提供准确点预测和可靠不确定性。
AI 中文摘要
对多个相互关联的环境变量（如区域降水和温度或其他相关地球物理场）在多个地点进行可靠预测，需要准确预测并伴有可靠的不确定性声明。现代深度学习模型能准确预测但通常不报不确定性，通过最大似然法强制输出不确定性会降低准确性。为此，我们开发了TSCoNet，这是一种两阶段卷积循环模型，结合高斯Copula，在量化预测不确定性的同时联合预测多个变量的时空情况。该方法先学习准确的均值预测，然后固定均值，优化共享表示以估计预测方差，经标准重新校准后产生校准后的预测区间，在不牺牲点精度的情况下增加不确定性。我们在球体上的模拟非平稳空间场以及2000 - 2020年五十个城市的月降水和温度真实数据集上研究该方法。该模型在提供确定性模型无法提供的校准预测区间的同时，与强大的确定性预测器的准确性相匹配，为多变量时空数据提供了兼具准确点预测和可靠不确定性的单一工具。
英文摘要
Reliable forecasting of several interrelated environmental variables - such as regional precipitation and temperature, or other correlated geophysical fields - across many locations calls for accurate predictions accompanied by trustworthy statements of their uncertainty. Modern deep-learning models forecast such variables accurately but usually report no uncertainty, and forcing them to output uncertainty through maximum likelihood tends to degrade their accuracy, especially when the variables are strongly correlated. Motivated by this tension, we develop TSCoNet, a two-stage convolutional-recurrent model coupled with a Gaussian copula that jointly forecasts multiple variables over space and time while quantifying predictive uncertainty. The method first learns accurate mean forecasts and then, holding the mean fixed, refines a shared representation to estimate the predictive variance, yielding calibrated prediction intervals after a standard recalibration, so that uncertainty is added without sacrificing point accuracy. We study the approach on simulated non-stationary spatial fields on the sphere and on a real dataset of monthly precipitation and temperature for fifty cities over 2000-2020. The model matches the accuracy of a strong deterministic forecaster while supplying calibrated prediction intervals that the deterministic model cannot, giving a single tool that provides both accurate point forecasts and reliable uncertainty for multivariate spatio-temporal data.
