From partial data to out-of-sample parameter and observation estimation with diffusion maps and geometric harmonics

A data-driven framework is presented, that enables the prediction of quantities, either observations or parameters, given sufficient partial data. The illustrated via a computational model deposition Cu in Chemical Vapor Deposition (CVD) reactor, where reactor pressure, temperature and feed mass flow rate are important process parameters determine outcome process. sampled high-dimensional vectors containing outputs detailed CFD steady-state process, i.e. values velocity, temperature, species fractions at each point discretization. machine learning workflow able to predict out-of-sample (a) (e.g. fraction reactor), inlet temperature); (b) observation data; (c) other reactor). proposed relies on two manifold schemes: Diffusion Maps associated Geometric Harmonics. used for discovering reduced representation available data, Harmonics extending functions defined discovered manifold. In our work special use case formulated implemented, which we call Double Maps, map from back (partial) parameters. comparison scheme traditional Gappy-POD approach provided: ours can be thought as “Gappy DMAP” approach. presented methodology easily transferable application domains beyond engineering.