  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.
