Invited talk by Stefano Marelli
Events
Stefano Marelli gives a talk entitled “Compressive polynomial chaos expansions for high-dimensional-output models” at the Workshop “The Next Generation of Surrogate Modelling in Environmental Science” organized by Lancaster University (Bailrigg, UK).
More information about the workshop can be found external pageherecall_made.
Abstract
Dealing with high-dimensional problems is a highly active branch of research in the uncertainty quantification community. However, most of the focus is on reducing the dimensionality of the input parameter space, rather than the output.
Modern high-resolution numerical models are often characterized by high-dimensional maps of outputs though (e.g. nodal displacements on a FEM mesh), that may sometimes result in an extremely large number (e.g. >105) of highly correlated outputs for each realization of the input parameters.
Most of the available metamodelling techniques, however, are not yet suitable for handling such large maps, including polynomial chaos expansions (PCE). Indeed, the PCE of a numerical model with many outputs is traditionally handled by independently metamodelling each component. In this talk, I introduce a two-stage PCE approach that aims at solving this problem: in the first stage, PCE is used to compress the map of outputs on a much sparser basis in the natural coordinates of the map (e.g. latitude and longitude); in the second stage, standard PCE of the compressed map is carried out w.r.t. the underlying uncertain model parameters. Standard PCE post-processing techniques are then used to derive analytical expressions for several stochastic properties of the resulting compressive PCE.
An interesting property of this approach is that the compression stage can be applied to the output stage of any other surrogate model.