Non-parametric warping via local scale estimation for non-stationary Gaussian process modelling

We tackle the problem of reconstructing functions possessing highly heterogeneous behaviour across the input space from scattered evaluations. Our main approach combines non-stationary Gaussian process (GP) modelling with wavelet local analysis. A warped GP model is assumed, and a novel stationarization algorithm is proposed that relies on successive inverse warpings based on local scale estimation. The approach is applied to two mechanical case studies highlighting promising prediction performance compared to state-of-the-art methods.