Physically interpretable machine learning algorithm on multidimensional non-linear fields

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