The optimization of complex manufacturing processes, such as Chemical Vapor Deposition, requires integrated approaches that combine physical modeling with advanced data-driven methodologies. This review synthesizes recent advances in hybrid modeling frameworks that merge equation-based computational fluid dynamics, machine learning, and natural language processing models to enhance process understanding, prediction, optimization and control. In particular, natural language processing techniques are leveraged to generate embedding-based predictors that inform learning tasks. The proposed framework integrates data acquisition, dimensionality reduction, and feature engineering with contextual language processing embeddings, surrogate modeling, and sensitivity analysis. This results in improved forecasting accuracy and interpretability. Key applications include coating thickness prediction, process regime classification, and critical parameter identification using SHAP analysis and Sobol’ indices. Nevertheless, significant challenges remain, including limitations in sensor infrastructure, assessment of dataset sufficiency for specific industrial objectives, and restricted generalizability across reactor designs. This work highlights how hybrid frameworks, together with natural language processing models applied to industrial process datasets, can bridge the gap between data availability in industrial environments and the actionable insights required for practical implementation, while identifying necessary future directions for robust, scalable, and interpretable modeling systems in advanced manufacturing.

A moving-boundary FEM model describing isothermal drying of fruit was employed as an inverse problem to estimate water diffusivity and peel resistance, including shrinkage. Water diffusivity and peel resistance were estimated using the Levenberg-Marquardt (L-M) optimisation algorithm based on the experimental drying data. The surface resistance is accounted as the sum of the peel and the diffusive boundary layer resistances, the latter being negligible compared to the former. The estimated peel resistance decreased by 86% as the drying temperature increased from 45 °C to 65 °C and by 44% as the drying temperature increases from 55 °C to 65 °C. The CFD optimisation model efficiently predicted the experimental water content and shrinkage.

This study introduces a machine learning framework tailored to large-scale industrial processes characterized by a plethora of numerical and categorical inputs. The framework aims to (i) discern critical parameters that influence the output and (ii) generate accurate out-of-sample qualitative and quantitative predictions of production outcomes. Specifically, we address the pivotal question of the significance of each input in shaping the process outcome, using an industrial Chemical Vapor Deposition (CVD) process as an example. The initial objective involves merging subject matter expertise and clustering techniques exclusively on the process output, here, coating thickness measurements at various positions in the reactor. This approach identifies groups of production runs that share similar qualitative characteristics, such as film mean thickness and standard deviation. In particular, the differences of the outcomes represented by the different clusters can be attributed to differences in specific inputs, indicating that these inputs are potentially critical to the production outcome. Shapley value analysis corroborates the formed hypotheses. Leveraging this insight, we subsequently implement supervised classification and regression methods using the identified critical process inputs. The proposed methodology proves to be valuable in scenarios with a multitude of inputs and insufficient data for the direct application of deep learning techniques, providing meaningful insights into the underlying processes.

This study presents a Bayesian framework for (inverse) uncertainty quantification and parameter estimation in a two-step Chemical Vapor Deposition coating process using production data. We develop an XGBoost surrogate model that maps reactor setup parameters to coating thickness measurements, enabling efficient Bayesian analysis while reducing sampling costs. The methodology handles a mixture of data including continuous, discrete integer, binary, and encoded categorical variables. We establish parameter prior distributions through Bayesian Model Selection and perform Inverse Uncertainty Quantification via weighted Approximate Bayesian Computation with summary statistics, providing robust parameter credible intervals while filtering measurement noise across multiple reactor locations. Furthermore, we employ clustering methods guided by geometry embeddings to focus analysis within homogeneous production groups. This integrated approach provides a validated tool for improving industrial process control under uncertainty.

Important variables of processes are often categorical, i.e. names or labels representing, e.g. categories of inputs, or types of reactors or a sequence of steps. In this work, we use Natural Language Processing Models to derive embeddings of such inputs that represent their actual meaning, or reflect the "distances" between categories, i.e. how similar or dissimilar they are. This is a marked difference from the current standard practice of using binary, or one-hot encoding to replace categorical variables with sequences of ones and zeros. Combined with dimensionality reduction techniques, either linear such as Principal Component Analysis, or nonlinear such as Uniform Manifold Approximation and Projection, the proposed approach leads to a meaningful, low-dimensional feature space. The significance of obtaining meaningful embeddings is illustrated in the context of an industrial coating process for cutting tools that includes both numerical and categorical inputs. In this industrial process, subject matter expertise suggests that the categorical inputs are critical for determining the final outcome but this cannot be taken into account with the current state-of-the-art. The proposed approach enables feature importance which is a marked improvement compared to the current state-of-the-art in the encoding of categorical variables. The proposed approach is not limited to the case-study presented here and is suitable for applications with similar mix of categorical and numerical critical inputs.

Food drying is a storage process during which the available water is removed. The present analysis conducted for three drying temperatures 45, 55 and 65 °C and the effective water diffusivity was estimated as 1.69×10-10, 2.91×10-10 and 6.67×10-10 m2/s. Comsol Multiphysics 4.3b was used to model the problem and simulate the process. The apricot hemispheres shrinkage was modelled as function of moisture content reduction. The results showed that water diffusivity, the mass transfer coefficient between the fruit surface and drying air and the activation energy of the process increase with drying temperature. The mass transfer coefficient, km, was estimated as 1.0×10-5, 9.98×10-5 and 0.85×10-2 m/s at 45, 55 and 65 °C. The estimated activation energy was 59.6, 59.9 and 60.8 kJ/mol at 45, 55 and 65 °C. The average relative error between experimental and computational moisture content was 0.47, 0.88 and 1.32% at 45, 55 and 65 °C. The Levenberg-Marquardt (L-M) and Sparse Non-Linear Optimizer (SNOPT) optimization algorithms were implemented.

Carbonation precipitation processes have been widely used due to their numerous applications in a wide range of fields. The complexity of these processes lies within the interplay of transport phenomena, multiphase flows, chemical reactions, and solid precipitation, deeming the experimental analysis and in-depth mechanistic understanding of the process dynamics a rather challenging task. In this work, a three-dimensional CFD model is developed, focusing on the carbonation step of the carbonation precipitation process, taking into account the flow dynamics of the liquid solution in the stirred tank, the CO2 bubble flow, and the dissolution in the liquid solution, as well as its dissociation in water. The model is validated with experimental measurements, and a very good agreement is achieved. Additionally, a parametric analysis is conducted to study the effect of different process parameters, such as temperature, CO2 flow rate, and rotational speed. The analysis of the different phenomena and their interplay reveals the key mechanisms that dictate the carbonation step, resulting in an in-depth understanding of the process. The presented computational approach can potentially pave the way towards a knowledge-based process and reactor design; thus, assisting the scale-up of such processes in stirred tank reactors.

This work introduces a comprehensive approach utilizing data-driven methods to elucidate the deposition process regimes in Chemical Vapor Deposition (CVD) reactors and the interplay of physical mechanism that dominate in each one of them. Through this work, we address three key objectives. Firstly, our methodology relies on process outcomes, derived by a detailed CFD model, to identify clusters of “outcomes” corresponding to distinct process regimes, wherein the relative influence of input variables undergoes notable shifts. This phenomenon is experimentally validated through Arrhenius plot analysis, affirming the efficacy of our approach. Secondly, we demonstrate the development of an efficient surrogate model, based on Polynomial Chaos Expansion (PCE), that maintains accuracy, facilitating streamlined computational analyses. Finally, as a result of PCE, sensitivity analysis is made possible by means of Sobol’ indices, that quantify the impact of process inputs across identified regimes.The insights gained from our analysis contribute to the formulation of hypotheses regarding phenomena occurring beyond the transition regime. Notably, the significance of temperature even in the diffusion-limited regime, as evidenced by the Arrhenius plot, suggests activation of gas phase reactions at elevated temperatures. Importantly, our proposed methods yield insights that align with experimental observations and theoretical principles, aiding decision-making in process design and optimization. By circumventing the need for costly and time-consuming experiments, our approach offers a pragmatic pathway toward enhanced process efficiency. Moreover, this study underscores the potential of data-driven computational methods for innovating reactor design paradigms.

This work introduces a machine learning framework that allows the investigation of the influence of reaction centers on the metabolic state of astrocyte cells. The proposed ML framework takes advantage of spatial astrocyte metabolic data stemming from numerical simulations for different reaction center configurations and allows for the following: (i) Discovery of cell groups of similar metabolic states and investigation of the reaction center configuration within each group. This approach allows for an analysis of the importance of the specific location of the reaction centers for a potentially critical metabolic state of the cell. (ii) Qualitative prediction of the energetic state of the cell (based on [ATP]: [ADP]) and quantitative prediction of the metabolic state of the cell by predicting the spatial average concentration of the metabolites or the complete spatial metabolic profile within the cell. (iii) Finally, the framework allows for the post hoc analysis of the developed quantitative predictive models using a SHAP approach to investigate the influence of the reaction center positions for further support of the insights drawn in steps (i)-(iii). Following the implementation of the framework, we observe that a uniform mitochondrial distribution within the cell results in the most robust energetic cell state. On the contrary, realizations of polarized mitochondrial distributions exhibit the worst overall cell health. Furthermore, we can make accurate qualitative predictions regarding cell health (accuracy=0.9515, recall=0.9753) and satisfactory predictions for the spatial average concentration and spatial concentration profiles of most of the metabolites involved. The techniques proposed in this study are not restricted to the dataset used. They can be easily used in other datasets that include findings from various metabolic computational models. ### Competing Interest Statement The authors have declared no competing interest.

Computational 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.

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.

Self-sustained periodic flows can be found in the laminar flow regime of a vertical, stagnation point CVD reactor. Here, we examine the effect of flow periodicity on the thickness non-uniformity of the deposited films. The case study is silicon (Si) deposition and we perform transient simulations by solving the continuity, momentum, energy and species transport equations in order to compute the film thickness and uniformity on a single wafer for different operating conditions. The Arrhenius plot of the process is constructed to identify the different regimes of deposition. Our results reveal that CVD process under self-sustained periodic flows produces highly non-uniform films which are dysfunctional for practical applications.

A 2D cross-field plasma fluid model (CFPM) is applied to He and He/O 2 discharges in the CΟoperation in Science and Technology (COST) reference microplasma jet to investigate the operating modes, namely α-, α – γ , and γ -mode. The model not only captures the measured spatiotemporal behavior of He excitation to He metastable but also quantitatively predicts measured power–voltage (PV) characteristics for He/O 2 discharges; although not addressed by previous studies, this is a prerequisite for the reliability of the model predictions for the critical-for-applications densities of reactive species. Through a comparison to time-averaged emission profiles and allowed by the dimensionality of the CFPM, the localized, close to the outlet of the discharge channel, onset of γ -mode for He discharges is predicted and justified. Τhe sheath boundary is defined by the maximum of the electron density derivative and the model results compare well to measurements of time-averaged sheath width. Criteria for the transition between the operating modes are formulated. It is considered that when the production rate of He metastable in the sheaths reaches 10% of its total production rate, transition from α- to α – γ mode takes place. When this percentage reaches ∼50%, i.e. α- and γ- modes have an almost equal contribution to the discharge, the electron temperature becomes maximum. Finally, the sensitivity of PV characteristics on the secondary electron emission coefficients, condition of the electrode surface, and fabrication or assembly mishits of the COST jet, is investigated.

An 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.

The analysis, development, and implementation of novel complex industrial crystallization processes requires kinetic knowledge of not only crystal growth and nucleation but also breakage, dissolution, and agglomeration processes. In this work, the crystal growth, dissolution, and agglomeration kinetics of sodium chlorate (NaClO3) in aqueous solutions are estimated via seeded batch experiments with in-line particle size distribution measurements. Contrary to previous works, the growth/dissolution kinetics are expressed in terms of the fundamental driving force of crystallization calculated from the activity of supersaturated solutions. The activity-based driving force is roughly 2-fold higher than the commonly used representation, which assumes ideal solutions. By fitting experimental desupersaturation data to mechanistic and empirical growth models, we show that the growth of sodium chlorate is surface integration controlled and is best described by a two-dimensional birth and spread surface nucleation mechanism. The dissolution of sodium chlorate crystals is diffusion controlled and is similar to 4 times faster than the growth at an equal initial driving force. Particle agglomeration is substantial in the early stages of crystallization experiments, likely due to a strong increase in the particle number due to initial breeding secondary nucleation upon seeding. The agglomeration rate constant increases with supersaturation and decreases at higher energy dissipation rate (by increased agitation) due to a strong decrease in the efficiency of interparticle collisions. Seeding with material of different sizes does not influence the agglomeration rate constant, although substantial amount of small particles was present in all seeding materials.

The problem of mixing of solutions of biomolecules in the famous staggered herringbone micromixer (SHM) is revisited through a computational study with the focus on two overlooked aspects, namely the accuracy of the numerical solution and the thorough analysis of the mixing process. The study is based on the numerical solution of the continuity and Navier-Stokes equations and the mass balance of the solute. The numerical instabilities, induced by the high Pe?clet number (extremely low diffusion coefficient of biomolecules), are handled with stabilization methods and the accuracy is ensured by a) dense adaptive meshes constructed by an error criterion and b) systematic studies of the mesh independence of the numerical solution. The importance of the accuracy on the calculated mixing efficiency (ME) and the design of the SHM is demonstrated through a comparison with the results for non-adaptive and coarse meshes. The ME versus the length of the SHM is compared with experimental data for the first time, with the mesh independent solution in good agreement with them. The thorough analysis brings to light symmetries and periodicities in the velocity field and explains the inflection point of the ME versus the length of the SHM, observed in experimental and computational studies. Without an optimization algorithm, designs which increase the ME up to 100% and reduce the mixing length are proposed. In particular, the mixing length is reduced a) by 8% through the introduction of symmetric grooves in the SHM, b) up to 39%, if the bottom of the SHM is made slippery, and c) up to 49% by adding symmetric grooves in case (b). The effect of the designs on the chaotic advection is demonstrated.

Monte Carlo (MC) and kinetic Monte Carlo (kMC) models are widely used for studying the physicochemical surface phenomena encountered in most deposition processes. This spans from physical and chemical vapor deposition to atomic layer and electrochemical deposition. MC and kMC, in comparison to popular molecular methods, such as Molecular Mechanics/Dynamics, have the ability to address much larger time and spatial scales. They also offer a far more detailed approach of the surface processes than continuum-type models, such as the reaction-diffusion models. This work presents a review of the modern applications of MC/kMC models employed in deposition processes.

When two granular phases are brought into motion in a rotating drum, a competition of mixing and segregation occurs. Several image analysis methods have been used to quantify the mixing. In this work, a modification of the contact method, originally proposed by Van Puyvelde et al. (Powder Technol. 106, 183–191 (1999)), is suggested to allow evaluation of the mixing index for each separate image. A strength of this modified method lies in the removal of the case-dependent normalization of the mixing index, which has so far impaired a direct comparison to other studies. This modified method is tested on artificial and experimental images of a granular bed composed of spherical glass and polypropylene beads of equal size. The bed evolves in a rotating drum under the rolling regime. The temporal evolution of the mixing index is in excellent agreement with the commonly used variance method.

A chemical reaction model, consisting of two gas-phase and a surface reaction, for the deposition of copper from copper amidinate is investigated, by comparing results of an efficient, reduced order CFD model with experiments. The film deposition rate over a wide range of temperatures, 473K-623K, is accurately captured, focusing specifically on the reported drop of the deposition rate at higher temperatures, i.e above 553K that has not been widely explored in the literature. This investigation is facilitated by an efficient computational tool that merges equation-based analysis with data-driven reduced order modeling and artificial neural networks. The hybrid computer-aided approach is necessary in order to address, in a reasonable time-frame, the complex chemical and physical phenomena developed in a three-dimensional geometry that corresponds to the experimental set-up. It is through this comparison between the experiments and the derived simulation results, enabled by machine-learning algorithms that the prevalent theoretical hypothesis is tested and validated, illuminating the possible underlying dominant phenomena. (C) 2021 Elsevier Ltd. All rights reserved.

Chemical vapor deposition (CVD) is an established process for the production of thin solid films for industrial and scientific applications for more than 30 years. CVD is a multiscale process; the process per se takes place in a reactor of the order of cm or even m in average linear size, but the properties of the end product, i.e. the deposited film, refer to micro-/nano- or even atomic scales. Two important cases can be distinguished: (1) deposition over a patterned surface consisting of features such as trenches or holes with dimensions from μm to tens of nm and (2) deposition over an initially flat surface and subsequent growth of nano-/micro-roughness on the film surface. Based on these cases, over the years, several multiscale models and methodologies have been proposed for the design, analysis and optimization of the CVD process taking into account information from the different scales. In this work, we review these multiscale models and methodologies in terms of the individual models that have been used in each scale, the linking or coupling between the models and the information that is transferred from one scale to another, and the parallel computing techniques accelerating the computations.