MANIFOLD LEARNING-BASED POLYNOMIAL CHAOS EXPANSIONS FOR HIGH-DIMENSIONAL SURROGATE MODELS

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of set high-dimensional data representing quantities interest computational or analytical model. For purpose, employ Grassmannian diffusion maps, two-step nonlinear dimension reduction technique which allows us reduce dimensionality and meaningful geometric descriptions parsimonious inexpensive manner. Polynomial chaos expansion then used construct mapping between stochastic input parameters coordinates reduced space. An adaptive clustering proposed an optimal number clusters points latent The similarity harmonic emulators are finally utilized as pre-trained models perform inverse map realizations features ambient space thus accurate out-of-sample predictions. Thus, acts encoder-decoder system able automatically handle very while simultaneously operating successfully small-data regime. demonstrated on two benchmark problems advection-diffusion-reaction equations model first-order chemical reaction species. all test cases, achieve highly approximations ultimately lead significant acceleration UQ tasks.