Physically interpretable machine learning algorithm on multidimensional non-linear fields

•Polynomial Chaos Expansion is efficient as Machine Learning (ML).•It is coupled to Proper Orthogonal Decomposition (POD) for multidimensional fields.•POD-PCE is presented as a single-layered feedforward Neural Network (NN).•Successfully compared to classical NN, while being linear and interpretable.•Adequate ranking indices can be used for physical insights on the studied problem.