Machine Learning Seminar presentation
Topic: From partial data to out-of-sample parameter and observation estimation with Diffusion Maps and Geometric Harmonics
Speaker: Dr. Eleni Koronaki, University of Luxembourg, Department of Computational Science
Time: Wednesday 2020.12.09, 10:00 CET
How to join: Please contact Jakub Lengiewicz
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.