Physics-agnostic and Physics-infused machine learning for thin films flows: modeling, and predictions from small data

Numerical simulations of multiphase flows are crucial in numerous engineering applications, but are often limited by the computationally demanding solution of the Navier-Stokes (NS) equations. Here, we present a data-driven workflow where a handful of detailed NS simulation data are leveraged into a reduced-order model for a prototypical vertically falling liquid film. We develop a physics-agnostic model for the film thickness, achieving a far better agreement with the NS solutions than the asymptotic Kuramoto-Sivashinsky (KS) equation. We also develop two variants of physics-infused models providing a form of calibration of a low-fidelity model (i.e. the KS) against a few high-fidelity NS data. Finally, predictive models for missing data are developed, for either the amplitude, or the full-field velocity and even the flow parameter from partial information. This is achieved with the so-called "Gappy Diffusion Maps", which we compare favorably to its linear counterpart, Gappy POD

Nonlinear dimensionality reduction then and now: AIMs for dissipative PDEs in the ML era

This study presents a collection of purely data-driven workflows for constructing reduced-order models (ROMs) for distributed dynamical systems. The ROMs we focus on, are data-assisted models inspired by, and templated upon, the theory of Approximate Inertial Manifolds (AIMs); the particular motivation is the so-called post-processing Galerkin method of Garcia-Archilla, Novo and Titi. Its applicability can be extended: the need for accurate truncated Galerkin projections and for deriving closed-formed corrections can be circumvented using machine learning tools. When the right latent variables are not a priori known, we illustrate how autoencoders as well as Diffusion Maps (a manifold learning scheme) can be used to discover good sets of latent variables and test their explainability. The proposed methodology can express the ROMs in terms of (a) theoretical (Fourier coefficients), (b) linear data-driven (POD modes) and/or (c) nonlinear data-driven (Diffusion Maps) coordinates. Both Black-Box and (theoretically-informed and data-corrected) Gray-Box models are described; the necessity for the latter arises when truncated Galerkin projections are so inaccurate as to not be amenable to post-processing. We use the Chafee-Infante reaction-diffusion and the Kuramoto-Sivashinsky dissipative partial differential equations to illustrate and successfully test the overall framework.Comment: 27 pages, 22 figure

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

peer reviewedA 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

Investigation of reaction mechanisms in the chemical vapor deposition of al from DMEAA

We propose a novel reaction scheme for the chemical vapor deposition (CVD) of Al films on substrates from dimethylethylamine alane (DMEAA), supported by the prediction of the Al deposition rate as a function of process temperature. The scheme is based on gas phase oligomerizations of alane which form a substantial amount of intermediates. Combined with reversible surface dehydrogenation steps, the global deposition reaction is composed of a set of 12 chemical reactions. This new scheme entails four intermediates and includes side reactions that play an important role in the formation of Al thin films. The chemistry mechanism is incorporated in a 2D Computational Fluid Dynamics (CFD) model of the CVD reactor setup used for the experimental investigation. The simulation predictions of the Al deposition rate are in good agreement with corresponding experimental measurements. The success of this novel reaction pathway lies in its ability to capture the abrupt decrease of the deposition rate at temperatures above 200 °C, which is attributed to the gas phase consumption of alane along with its increased desorption rate from the film surface

Equation-based and data-driven modeling strategies for industrial coating processes

peer reviewedComputational Fluid Dynamics (CFD) and Machine Learning (ML) approaches are implemented and compared in an industrial Chemical Vapor Deposition process for the production of cutting tools. In this work, the aim is to analyze the pros and cons of each method and propose a blend of the two approaches that is suitable in industrial applications, where the process is too complicated to address with first-principles models and the data do not allow the implementation of data-hungry methods. Both approaches accurately predict the coating thickness (Mean Absolute Percentage Error (MAPE) of 6.0% and 4.4% for CFD and ML respectively for the test case reactor). CFD, despite its increased computational cost, both in terms of developing and also calibrating for the application at hand, provides meaningful insight and illuminates the process. On the other hand, ML can provide predictions in a time-efficient manner, and is thus appropriate for inline and concurrent predictions. However, it is limited by the available data and has low extrapolation ability. Equation-based and data-driven methods are combined by exploiting a handful of CFD results for efficient interpolation in a reduced space defined by the principal components of the dataset, by implementing Gappy POD. This allows for the accurate reconstruction of the full state-space with limited data.U-AGR-7130 - BRIDGES/21/16758846/OptiSimCVD (01/06/2022 - 31/05/2026) - BORDAS Stéphan

An efficient chemistry-enhanced CFD model for the investigation of the rate-limiting mechanisms in industrial Chemical Vapor Deposition reactors

peer reviewedAn efficient CFD model for the deposition of alumina from a gas mixture consisting of AlCl3, CO2, HCl, H2 and H2S in an industrial CVD reactor with multiple disks and a rotating feeding tube, is proposed. The goal is twofold: (i) to predict the thickness of the deposited material, (ii) to investigate whether the process rate is determined by the reaction rate or by diffusion. A reaction model that consists of a gas-phase homogeneous reaction and a heterogeneous reaction is implemented, with a proposed kinetics rate that includes the effect of the H2S concentration. The latter has a catalytic effect, but the mechanism is not entirely understood. The entire reactor geometry (consisting of 40–50 perforated disks) is divided into appropriately chosen 7-disk sections. The 2D, time-dependent CFD model is validated using production data for the deposition thickness. The proposed computational tool delivers accurate predictions (average relative error 5%) for different geometries corresponding to real reactor set-ups. Extending the functionality beyond prediction, a computational experiment is performed to illuminate the interplay between species diffusion and chemical reaction rates, which determines the rate-limiting mechanism. The results indicate that species diffusion is fast enough and therefore reaction kinetics determine the overall deposition rate.R-AGR-3747 - BRIDGES/HybridSimCVD - Ceratizit Contrib (01/03/2020 - 28/02/2022) - BORDAS Stéphan