Data-driven nonlinear manifold learning for model order reduction, interpolation and regression in complex processes
Speaker: Eleni Koronaki (Faculty of Science, Technology and Medicine; University of Luxembourg)
Title: Data-driven nonlinear manifold learning for model order reduction, interpolation and regression in complex processes
Time: Wednesday, 2020.12.09, 10:00 a.m. (CET)
Place: fully virtual (contact Dr. Jakub Lengiewicz to register)
Format: 30 min. presentation + 30 min. discussion
Abstract:
A data-driven framework is presented, that enables the estimation of quantities, either observations or parameters, given enough partial data. Here the data are high-dimensional vectors containing the outputs of a detailed CFD model of the process, i.e. the values of velocity, pressure, temperature and species mass fractions at each point in the discretization. The goal is to predict the outputs of new inputs, here process parameters and also the inputs that correspond to new outputs. Finally, along the lines of a nonlinear observer, part of the outputs are predicted given only a limited number of partial observations, i.e. not the entire output vector but rather a handful of independent values. The proposed workflow begins by determining the intrinsic reduced description of the available data with Diffusion Maps, a data-driven nonlinear manifold learning technique that can be thought of as the nonlinear counterpart of Principal Components Analysis. This low-dimensional description of the high dimensional ambient space that contains the data, is then leveraged for efficient interpolation and regression with a special implementation of Geometric Harmonics.