In an ever-increasing interest for Machine Learning (ML) and a favorable data development context, we here propose an original methodology for data-based prediction of two-dimensional physical fields. Polynomial Chaos Expansion (PCE), widely used in the Uncertainty Quantification community (UQ), has long been employed as a robust representation for probabilistic input-to-output mapping. It has been recently tested in a pure ML context, and shown to be as powerful as classical ML techniques for point-wise prediction. Some advantages are inherent to the method, such as its explicitness and adaptability to small training sets, in addition to the associated probabilistic framework. Simultaneously, Dimensionality Reduction (DR) techniques are increasingly used for pattern recognition and data compression and have gained interest due to improved data quality. In this study, the interest of Proper Orthogonal Decomposition (POD) for the construction of a statistical predictive model is demonstrated. Both POD and PCE have amply proved their worth in their respective frameworks. The goal of the present paper was to combine them for a field-measurement-based forecasting. The described steps are also useful to analyze the data. Some challenging issues encountered when using multidimensional field measurements are addressed, for example when dealing with few data. The POD-PCE coupling methodology is presented, with particular focus on input data characteristics and training-set choice. A simple methodology for evaluating the importance of each physical parameter is proposed for the PCE model and extended to the POD-PCE coupling.

在对机器学习（ML）的兴趣不断增长和有利的数据开发环境下，我们在此提出一种用于基于数据的二维物理场预测的原始方法。不确定性量化社区（UQ）中广泛使用的多项式混沌扩展（PCE）长期以来一直被用作概率输入到输出映射的可靠表示。最近，它已在纯ML上下文中进行了测试，并显示出与经典ML技术一样强大的逐点预测能力。该方法具有一些固有的优势，例如，与关联的概率框架相比，它的明确性和对小型训练集的适应性。同时，降维（DR）技术越来越多地用于模式识别和数据压缩，并且由于提高了数据质量而引起了人们的兴趣。在这项研究中，证明了适当的正交分解（POD）对构建统计预测模型的兴趣。POD和PCE都在各自的框架中充分证明了自己的价值。本文的目的是将它们结合起来以进行基于现场测量的预测。所描述的步骤对于分析数据也很有用。解决了使用多维场测量时遇到的一些具有挑战性的问题，例如在处理少量数据时。提出了POD-PCE耦合方法，特别关注输入数据特征和训练集选择。