Multilevel Monte Carlo for noise estimation in stochastic multiscale systems

Kimaev, Grigoriy; Ricardez‐Sandoval, Luis A.

doi:10.1016/j.cherd.2018.10.006

Cited by 7 publications

(3 citation statements)

References 48 publications

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“…However, a complete description of this stochastic multiscale system can be found elsewhere. 20,21,31,32,43,44,80 The model has been observed to agree with experimental results. 2,81,82 The macroscale simulation is comprised of momentum, energy and mass transport partial differential equations (PDEs), which are coupled with the microscale kMC code via a boundary condition.…”

Section: ■ Theoretical Methodssupporting

confidence: 73%

“…In this section, we present a condensed summary of the model of thin film production by CVD used in this work as a case study. However, a complete description of this stochastic multiscale system can be found elsewhere. ,,,,,, The model has been observed to agree with experimental results. ,, …”

Section: Theoretical Methodsmentioning

confidence: 58%

“…Consequently, shrinking horizon NMPC was applied to the CVD model to find the optimal time-dependent T surf and X bulk that would achieve the requirements in R kMC and Gr kMC under uncertainty. Equation contains the NMPC scheme that maximizes Gr kMC throughout the production batch while satisfying the maximum acceptable final R kMC constraint: where t i represents the sampling times at the end of every sampling interval, n is the total number of sampling intervals, Δ t is the length of the sampling intervals, and f CVD is the CVD model subject to time-invariant uncertainty in the parameter E , which is the energy associated with a single bond between atoms in the thin film. ,,,,,, In addition, R * is the maximum tolerance on R kMC at the end of the batch, T min and T max are the minimum and maximum bounds on T surf , respectively, and X min and X max are the minimum and maximum bounds on X bulk , respectively. T 0 and X 0 are the initial conditions for T surf and X bulk , respectively, and Δ T and Δ X are the maximum allowed perturbations in T surf and X bulk between the adjacent sampling intervals.…”

Section: Theoretical Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Artificial Neural Network Discrimination for Parameter Estimation and Optimal Product Design of Thin Films Manufactured by Chemical Vapor Deposition

Kimaev

Ricardez‐Sandoval

2020

J. Phys. Chem. C

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Industrial production of valuable chemical products often involves the manipulation of phenomena evolving at different temporal and spatial scales. Product properties can be captured accurately using computationally expensive stochastic multiscale models that explicitly consider the feedbacks between different scales. However, product design quality is often tampered by uncertainties affecting process operation. In this work, we used artificial neural networks (ANNs) to estimate an uncertain parameter, accurately predict product properties under uncertainty, and achieve orders-of-magnitude computational savings of a multiscale model of thin film formation by chemical vapor deposition. ANNs were trained using multiple realizations of the uncertain parameter to capture the behavior of the thin film’s two key microscale properties: roughness and growth rate. Next, mean square error and maximum likelihood estimation were used for parameter estimation and to find the ANN that could generate the closest predictions to the real-time measurements collected from the process in the presence of uncertainty. The chosen ANNs were employed to seek for the optimal operating conditions to enable the fabrication process to meet product quality specifications. ANNs are a promising technique for product property prediction and efficient decision making in the design of optimal operating conditions for chemical processes under uncertainty.

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Section: ■ Theoretical Methodssupporting

confidence: 73%

Section: Theoretical Methodsmentioning

confidence: 58%

Section: Theoretical Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Artificial Neural Network Discrimination for Parameter Estimation and Optimal Product Design of Thin Films Manufactured by Chemical Vapor Deposition

Kimaev

Ricardez‐Sandoval

2020

J. Phys. Chem. C

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Uncertainty Quantification of Microstructures: A Perspective on Forward and Inverse Problems for Mechanical Properties of Aerospace Materials

Billah,

Elleithy,

Khan

et al. 2024

Adv Eng Mater

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In this review, state‐of‐the‐art studies on the uncertainty quantification (UQ) of microstructures in aerospace materials is examined, addressing both forward and inverse problems. Initially, it introduces the types of uncertainties and UQ algorithms. In the review, the forward problem of uncertainty propagation in process–structure and structure–property relationships is then explored. Subsequently, the inverse UQ problem, also known as the design under uncertainty problem, is discussed focusing on structure–process and property–structure linkages. Herein, the review concludes by identifying gaps in the current literature and suggesting key areas for future research, including multiscale topology optimization under uncertainty, implementing physics‐informed neural networks to UQ problems, investigating the effects of uncertainty on extreme mechanical behavior, reliability‐based design, and UQ in additive manufacturing.

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Multilevel Monte Carlo applied for uncertainty quantification in stochastic multiscale systems

2020

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The aim of this study is to evaluate the performance of multilevel Monte Carlo (MLMC) sampling technique for uncertainty quantification in stochastic multiscale systems. Two systems, a chemical vapor deposition chamber and a catalytic flow reactor, subject to multiple parameter uncertainty, were considered. The distributions of the systems' observables were estimated using standard MC sampling and polynomial chaos expansions (PCE), where the coefficients were calculated by nonintrusive spectral projection. The MLMC technique was used to efficiently sample the two systems and accurately estimate the data necessary for constructing the PCE expressions. The results show that the usage of MLMC improved the precision of identification of PCE versus the traditional heuristic approach and lowered the computational cost of uncertainty quantification compared to standard MC.

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Multilevel Monte Carlo for noise estimation in stochastic multiscale systems

Cited by 7 publications

References 48 publications

Artificial Neural Network Discrimination for Parameter Estimation and Optimal Product Design of Thin Films Manufactured by Chemical Vapor Deposition

Artificial Neural Network Discrimination for Parameter Estimation and Optimal Product Design of Thin Films Manufactured by Chemical Vapor Deposition

Uncertainty Quantification of Microstructures: A Perspective on Forward and Inverse Problems for Mechanical Properties of Aerospace Materials

Multilevel Monte Carlo applied for uncertainty quantification in stochastic multiscale systems

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