Chemical vapor deposition; Diffusion maps; Gappy POD; Geometric harmonics; Nonlinear manifold learning; Chemical vapour deposition; Mass-fraction; Non-linear manifold learning; Partial data; Partial observation; Process parameters; Work-flows; Chemical Engineering (all); Computer Science Applications; Mathematics - Numerical Analysis; Computer Science - Numerical Analysis; General Chemical Engineering
Abstract :
[en] A data-driven framework is presented, that enables the prediction of quantities, either observations or parameters, given sufficient partial data. The framework is illustrated via a computational model of the deposition of Cu in a Chemical Vapor Deposition (CVD) reactor, where the reactor pressure, the deposition temperature and feed mass flow rate are important process parameters that determine the outcome of the process. The sampled observations are high-dimensional vectors containing the outputs of a detailed CFD steady-state model of the process, i.e. the values of velocity, pressure, temperature, and species mass fractions at each point in the discretization. A machine learning workflow is presented, able to predict out-of-sample (a) observations (e.g. mass fraction in the reactor), given process parameters (e.g. inlet temperature); (b) process parameters, given observation data; and (c) partial observations (e.g. temperature in the reactor), given other partial observations (e.g. mass fraction in the reactor). The proposed workflow relies on two manifold learning schemes: Diffusion Maps and the associated Geometric Harmonics. Diffusion Maps are used for discovering a reduced representation of the available data, and Geometric Harmonics for extending functions defined on the discovered manifold. In our work a special use case of Geometric Harmonics is formulated and implemented, which we call Double Diffusion Maps, to map from the reduced representation back to (partial) observations and process parameters. A comparison of our manifold learning scheme to the traditional Gappy-POD approach is provided: ours can be thought of as a “Gappy DMAPs” approach. The presented methodology is easily transferable to application domains beyond reactor engineering.
Disciplines :
Chemical engineering
Author, co-author :
KORONAKI, Eleni ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE) ; School of Chemical Engineering, National Technical University of Athens, Attiki, Greece
Evangelou, Nikolaos ; Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, United States
Psarellis, Yorgos M. ; Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, United States
Boudouvis, Andreas G.; School of Chemical Engineering, National Technical University of Athens, Attiki, Greece
Kevrekidis, Ioannis G.; Department of Chemical and Biomolecular Engineering, Whiting School of Engineering, Johns Hopkins University, Baltimore, United States
External co-authors :
yes
Language :
English
Title :
From partial data to out-of-sample parameter and observation estimation with diffusion maps and geometric harmonics
The work of YGK, NE and YMP was partially supported by the US AFOSR FA9550-21-0317 and the US DOE SA22-0052-S001 . E.D.K. has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 890676 - DataProMat.The work of YGK, NE and YMP was partially supported by the US AFOSR FA9550-21-0317 and the US DOE SA22-0052-S001. E.D.K. has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 890676 - DataProMat.
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