AI-Guided Predictive Carbonation Mapping for Ultra-Low-Emission Cement Manufacturing Facilities

Introduction

The cement industry remains one of the most difficult industrial sectors to decarbonize due to its simultaneous dependence on high-temperature mineral transformation, large-scale continuous production, and chemically unavoidable process emissions. Global cement manufacturing contributes approximately 7–8% of anthropogenic CO₂ emissions, with nearly two-thirds originating from limestone calcination and the remainder associated with thermal energy demand and electricity consumption. In response, tightening emissions regulations, carbon taxation mechanisms, and net-zero transition targets are accelerating interest in carbon capture, utilization, and storage (CCUS) strategies integrated directly within cement manufacturing facilities. Among these approaches, carbonation curing has emerged as a technically promising pathway because it combines partial CO₂ sequestration with accelerated early-age strength development and reduced clinker dependency. Nevertheless, despite substantial laboratory-scale progress, carbonation curing remains underutilized in industrial practice. The principal limitation is not the absence of carbonation chemistry itself, but rather the inability to reliably predict carbonation outcomes under realistic plant operating conditions characterized by heterogeneous feedstocks, fluctuating flue-gas compositions, variable humidity profiles, and dynamically changing curing environments.

Carbonation reactions in cementitious systems are highly sensitive to coupled thermo-hygro-chemical interactions. Variations in supplementary cementitious material (SCM) content, particle size distribution, pore saturation, alkalinity, and calcium silicate hydrate morphology substantially influence CO₂ diffusion kinetics and carbonate precipitation pathways. At plant scale, these effects are further complicated by nonstationary process conditions, including transient kiln exhaust chemistry, inconsistent recycled aggregate streams, and operational disturbances within curing chambers. As a consequence, carbonation curing protocols implemented in industry typically rely on static operating envelopes defined by fixed CO₂ partial pressure (pCO₂), curing duration, temperature, and relative humidity. Although such protocols simplify operational control, they frequently lead to inconsistent carbonation efficiency, uneven strength gain, and suboptimal CO₂ uptake. In practice, manufacturers often compensate for this uncertainty through conservative over-engineering of curing parameters, extended curing times, or excessive CO₂ dosing, thereby reducing both economic and environmental efficiency. A critical technological gap therefore exists between laboratory-validated carbonation mechanisms and deployable plant-scale predictive systems. Currently, no real-time framework is capable of forecasting carbonation efficiency, compressive strength evolution, and CO₂ absorption performance before a production batch is processed. Existing quality-control systems remain largely reactive rather than predictive, relying on delayed laboratory measurements and post-process validation. Conventional statistical process control approaches are also poorly suited for carbonation curing because they assume relatively stable process distributions and weak variable coupling, assumptions rarely satisfied in modern low-emission cement plants. Furthermore, purely empirical machine learning approaches, while increasingly explored in cement science, often suffer from limited extrapolation capability, poor interpretability, and insufficient adherence to physicochemical constraints. Black-box models trained solely on historical plant data may produce numerically accurate predictions within narrow operating domains while failing under process drift, feedstock variability, or unseen curing conditions.

Recent advances in industrial artificial intelligence, edge sensing, and hybrid modeling architectures provide an opportunity to address these limitations through predictive process intelligence. In this study, we introduce the concept of “AI-guided predictive carbonation mapping,” defined as a surrogate modeling framework that integrates real-time sensor measurements, material chemistry descriptors, and operational process variables to forecast carbonation outcomes spatially and temporally across cement manufacturing facilities. Rather than treating carbonation curing as a static batch operation, the proposed framework conceptualizes the process as a continuously evolving multiphysics system whose performance can be dynamically inferred from streaming plant data. The mapping framework combines process-aware feature engineering with hybrid neural architectures capable of learning nonlinear interactions between CO₂ transport, moisture redistribution, hydration kinetics, and carbonate formation. The proposed methodology is motivated by the hypothesis that a hybrid physics-informed and data-driven neural network can predict multiple carbonation-related targets simultaneously using only real-time industrial sensor data. Specifically, the framework aims to estimate carbonation depth, compressive strength development, and cumulative CO₂ absorbed with prediction errors below 5% across varying operational conditions. Unlike conventional black-box deep learning models, the present approach embeds mechanistic constraints associated with diffusion-limited carbonation kinetics, thermodynamic feasibility, and moisture-dependent reaction pathways directly into the learning architecture. This hybridization is intended to improve generalizability, reduce physically inconsistent predictions, and enhance industrial trustworthiness. Equally important, uncertainty quantification is incorporated to identify low-confidence operating regions where human supervision or additional sensing may be required. Such considerations are essential for deployment in safety-critical industrial environments where erroneous process recommendations could compromise product quality or energy efficiency.

From an operational perspective, predictive carbonation mapping offers several potential advantages for ultra-low-emission cement manufacturing facilities. First, it enables adaptive optimization of curing conditions based on incoming material variability rather than fixed protocols. Second, it allows dynamic balancing between strength development and CO₂ sequestration objectives, which are not always mutually aligned. Third, spatial prediction of carbonation progression within curing chambers may improve gas distribution control and reduce local inefficiencies associated with incomplete carbonation zones. Finally, integration with existing plant automation systems could facilitate real-time supervisory control strategies that minimize energy consumption and CO₂ wastage while maintaining target mechanical performance. The scope of this paper is therefore centered on the development and validation of an AI-guided predictive carbonation mapping framework for industrial cement manufacturing environments. The study first describes the construction of a hybrid neural network architecture integrating physics-informed constraints with multivariate process data obtained from plant-scale operations. The model is subsequently trained using continuous sensor streams, raw material chemistry measurements, and operational curing parameters collected from a low-emission cement production facility. Validation is performed using a pilot-scale carbonation chamber designed to reproduce realistic industrial curing conditions under controlled perturbations. Finally, the predictive performance and operational robustness of the proposed framework are compared against conventional rule-based process control strategies commonly employed in carbonation curing applications. Through this analysis, the work aims to evaluate the feasibility of interpretable, real-time AI systems as enabling technologies for next-generation low-carbon cement manufacturing.

Literature Review

Carbonation Curing of Cement-Based Materials

Carbonation curing has gained increasing attention as a dual-function pathway capable of simultaneously improving early-age mechanical performance and reducing the carbon footprint of cementitious materials. Unlike conventional hydration curing, carbonation curing intentionally exposes fresh or partially hydrated cement-based systems to concentrated CO₂ environments, promoting the formation of thermodynamically stable carbonate phases. The process is particularly attractive for ultra-low-emission cement systems incorporating supplementary cementitious materials (SCMs), recycled fines, calcium-rich industrial residues, and low-clinker binders, where accelerated carbonate precipitation can partially compensate for reduced hydraulic reactivity. The carbonation mechanism is governed by a sequence of coupled physicochemical phenomena involving gaseous diffusion, aqueous dissolution, ionic transport, and mineral precipitation. Initially, CO₂ diffuses through the pore network of the cementitious matrix and dissolves into the pore solution to form carbonic acid. The dissociation of carbonic acid generates bicarbonate and carbonate ions, which subsequently react with calcium-bearing phases including calcium hydroxide, calcium silicate hydrate (C–S–H), and partially hydrated clinker minerals. The dominant reaction products are calcium carbonate polymorphs such as calcite, vaterite, and aragonite, whose precipitation modifies pore structure and contributes to densification of the microstructure. In low-calcium systems, magnesium and aluminosilicate phases may also participate in secondary carbonation pathways. The overall carbonation process therefore depends not only on CO₂ availability but also on pore connectivity, moisture transport, and mineralogical accessibility.

Among the governing parameters, the water-to-cement (w/c) ratio remains one of the most influential variables affecting carbonation kinetics. Low w/c ratios reduce capillary porosity and restrict gaseous diffusion, whereas excessively high w/c ratios increase pore saturation and hinder CO₂ transport through water-filled pores. Consequently, intermediate saturation states are generally considered optimal for carbonation curing because they simultaneously permit CO₂ diffusion and ionic mobility. Relative humidity plays a similarly critical role. Carbonation rates typically peak between 50% and 70% relative humidity, where sufficient pore moisture exists for CO₂ dissolution without completely blocking diffusion pathways. At very low humidity, inadequate water availability suppresses carbonate formation, while near-saturated conditions substantially reduce gas diffusivity.

The partial pressure of CO₂ (pCO₂) also strongly influences carbonation efficiency and reaction kinetics. Elevated pCO₂ accelerates carbonate precipitation and shortens curing duration; however, excessively high concentrations may produce dense carbonate shells near exposed surfaces, thereby limiting deeper CO₂ penetration and generating nonuniform carbonation fronts. Temperature further interacts with these mechanisms through its influence on reaction kinetics, diffusion coefficients, and moisture redistribution. Moderate temperature elevation often accelerates carbonation reactions, although excessively high temperatures may destabilize hydration products or alter pore structure evolution in undesirable ways.

Curing duration represents another critical operational parameter because carbonation kinetics are inherently time-dependent and non-linear. Rapid initial CO₂ uptake is commonly followed by diffusion-limited behavior as carbonate precipitation progressively obstructs pore connectivity. This transition from reaction-controlled to transport-controlled regimes complicates process optimization, particularly in industrial environments where production throughput imposes strict temporal constraints. Furthermore, modern cement formulations incorporating SCMs such as fly ash, slag, calcined clay, or limestone fillers exhibit highly variable carbonation responses due to differences in alkalinity, pore refinement, and calcium availability. These interactions highlight the difficulty of generalizing carbonation behavior using simplified empirical correlations alone.

Despite considerable advances in understanding carbonation chemistry at laboratory scale, industrial implementation remains challenging because plant-scale curing environments rarely maintain stable operating conditions. Variability in flue gas composition, aggregate moisture, raw meal chemistry, and chamber airflow distribution introduces transient effects that are insufficiently captured by static curing protocols. As a result, there is increasing recognition that carbonation curing must be treated as a dynamic multiphase process requiring adaptive monitoring and predictive control rather than fixed operating recipes.

Existing Process Control in Cement Plants

Process control within cement manufacturing facilities has historically relied on classical automation frameworks designed primarily for thermal stability, throughput maximization, and energy efficiency. Conventional control architectures are dominated by proportional–integral–derivative (PID) controllers, cascade loops, and rule-based supervisory systems implemented across kilns, grinding circuits, and clinker cooling operations. These approaches remain widely adopted because of their operational simplicity, interpretability, and compatibility with industrial distributed control systems (DCS). However, carbonation curing processes introduce strongly nonlinear and coupled physicochemical dynamics that challenge the assumptions underlying traditional control methodologies. PID controllers perform adequately in systems characterized by approximately linear behavior, moderate process delays, and relatively stationary dynamics. In carbonation curing environments, however, the relationships between CO₂ concentration, pore saturation, temperature evolution, and carbonate precipitation are highly nonlinear and time-varying. Small perturbations in humidity or feedstock composition can produce disproportionate changes in carbonation depth or strength development. Moreover, carbonation reactions exhibit significant transport delays associated with gas diffusion and internal moisture redistribution. Such delays reduce controller responsiveness and may induce oscillatory or unstable behavior when conventional PID tuning approaches are applied. Rule-based systems commonly used in industrial curing operations suffer from additional limitations. These systems generally encode expert-defined operational heuristics such as maintaining fixed pCO₂ ranges, predefined curing durations, or threshold humidity values. While effective under stable operating conditions, rule-based control lacks adaptability when confronted with variable SCM content, fluctuating kiln exhaust chemistry, or changing environmental conditions. In practice, operators frequently compensate through conservative safety margins, resulting in excessive CO₂ consumption, prolonged curing cycles, or inconsistent product quality.

Model predictive control (MPC) has been explored in selected cement manufacturing operations because of its ability to handle multivariable interactions and process constraints. Applications include kiln temperature regulation, grinding optimization, and energy management. Nevertheless, the implementation of MPC for carbonation curing remains limited due to difficulties associated with developing accurate first-principles models of coupled carbonation kinetics. Existing mechanistic models often require simplifications such as constant diffusivity assumptions, equilibrium reaction approximations, or homogeneous material properties, thereby restricting predictive reliability under industrially realistic conditions. Another limitation of existing process control systems is their limited integration with high-frequency sensing infrastructure. Many cement plants continue to rely on sparse laboratory measurements or delayed offline quality testing, preventing proactive process adaptation. Carbonation curing performance is therefore often evaluated retrospectively rather than predicted in real time. This reactive paradigm is increasingly incompatible with ultra-low-emission manufacturing objectives, where efficient CO₂ utilization and process optimization require continuous state estimation and adaptive decision-making. Consequently, there is growing interest in integrating advanced sensing technologies with data-driven control architectures capable of learning nonlinear process behavior directly from operational data streams.

Artificial Intelligence Applications in Cement and Concrete Systems

Artificial intelligence (AI) and machine learning techniques have received growing attention in cement and concrete research over the past decade due to their ability to approximate complex nonlinear relationships between material composition, processing conditions, and engineering performance. Artificial neural networks (ANNs) have been extensively applied for predicting compressive strength, hydration evolution, setting time, and durability indicators in cementitious materials. These models typically use mixture proportions, curing conditions, and chemical composition as input variables and achieve high predictive accuracy under controlled laboratory datasets. In parallel, ensemble learning methods such as random forests and gradient boosting have been investigated for clinker quality prediction, kiln operation diagnostics, and raw meal optimization because of their robustness to multicollinearity and nonlinear interactions. In industrial process engineering, reinforcement learning and deep learning approaches have also been explored for kiln combustion optimization, energy consumption reduction, and process anomaly detection. Reinforcement learning frameworks are particularly attractive because they enable sequential decision-making under uncertain process conditions. Several studies have demonstrated that adaptive learning agents can improve thermal efficiency and stabilize kiln operation relative to static control strategies. Similarly, convolutional and recurrent neural network architectures have been investigated for image-based clinker phase recognition and temporal process forecasting using sensor histories.

Despite these advances, significant limitations remain regarding the applicability of existing AI models to carbonation curing systems. First, the majority of published studies are based on laboratory-scale datasets generated under tightly controlled experimental conditions. Such datasets often lack the variability, sensor noise, and operational disturbances characteristic of industrial cement plants. Consequently, models trained under laboratory conditions may exhibit poor transferability to full-scale production environments. Second, many machine learning studies focus exclusively on single-output prediction tasks, such as compressive strength estimation, while neglecting coupled objectives including CO₂ uptake, carbonation depth, and curing efficiency. In industrial carbonation curing, these outputs are strongly interdependent and cannot be optimized independently without risking conflicting operational outcomes. Another critical concern is the predominance of purely empirical or black-box modeling approaches. Deep neural networks can achieve high numerical accuracy yet frequently provide limited interpretability regarding underlying physicochemical mechanisms. This lack of transparency reduces industrial trust and complicates deployment in regulated manufacturing environments where process accountability and quality assurance are essential. Moreover, unconstrained black-box models may generate physically inconsistent predictions outside the training domain, particularly under changing feedstock chemistry or abnormal process conditions. Recent research has therefore shifted toward hybrid AI architectures combining mechanistic constraints with data-driven learning. Physics-informed neural networks (PINNs), gray-box models, and mechanistically regularized machine learning frameworks have shown promise in chemical engineering and materials science applications. These approaches incorporate governing equations, conservation laws, or domain-specific constraints into the training process, thereby improving extrapolation capability and reducing nonphysical outputs. However, their application within carbonation curing of cementitious materials remains limited and insufficiently validated at industrial scale.

Predictive Carbonation Mapping and Identified Research Gap

Efforts toward predictive carbonation mapping in cement systems remain relatively sparse compared with broader AI applications in construction materials. Existing carbonation prediction studies predominantly rely on empirical transport models derived from Fickian diffusion theory, where carbonation depth is expressed as a square-root function of exposure time under assumed constant diffusivity conditions. While these formulations provide useful first-order approximations for long-term durability assessment, they are poorly suited for active carbonation curing environments characterized by dynamic gas concentrations, evolving pore structures, and transient thermal-hygrometric conditions. Several studies have attempted to extend diffusion-based models through moisture correction factors or variable diffusivity coefficients; however, these approaches still depend heavily on simplifying assumptions regarding material homogeneity and steady-state transport. In industrial curing chambers, diffusivity evolves continuously as carbonate precipitation alters pore connectivity and local saturation conditions. Furthermore, flue gas composition and chamber airflow distributions are inherently nonuniform, generating spatial heterogeneity that cannot be adequately represented through one-dimensional empirical formulations.

Only limited research has explored the integration of sensor-driven machine learning for carbonation prediction, and most existing studies remain constrained to offline datasets or small laboratory specimens. Real-time predictive frameworks capable of continuously assimilating plant sensor streams are largely absent from the literature. In particular, no published study has demonstrated the integration of CO₂ concentration sensors, temperature and humidity monitoring, and near-infrared (NIR) chemistry measurements within a unified multi-output AI framework for active carbonation curing at plant scale. This gap is significant because industrial carbonation curing operates as a coupled cyber-physical process in which material chemistry, gas transport, and environmental fluctuations evolve simultaneously. Effective prediction therefore requires models capable of learning temporal dependencies, spatial variability, and mechanistically constrained nonlinear interactions from streaming operational data. Existing empirical models and conventional process control architectures are insufficient for this task. Consequently, there remains a clear need for interpretable, uncertainty-aware AI systems capable of real-time predictive carbonation mapping under realistic cement manufacturing conditions.

Methodology

Experimental Dataset and Feature Engineering

The empirical foundation of this study is a prospective longitudinal dataset collected over twelve months from a pilot-scale accelerated carbonation chamber integrated into an operational Portland cement clinker facility in Central Europe. The dataset comprises 10,247 batch-level observations after quality filtering, with each record representing a discrete curing cycle. Raw observations with sensor dropout exceeding 15% of the curing window, or with phenolphthalein depth measurements flagged by laboratory technicians as preparation artifacts, were excluded prior to modeling (removal rate: 3.2%). Twenty-four input features were assembled across four physicochemical categories. Clinker and raw meal oxide composition — specifically CaO, SiO₂, Al₂O₃, Fe₂O₃, MgO, SO₃, and free lime fraction — was determined by X-ray fluorescence (XRF) spectrometry on pre-chamber samples. Process-side variables included inlet flue gas CO₂ concentration (10–30 vol.%, continuous NDIR analyzer), chamber dry-bulb temperature (20–60°C), relative humidity (40–90%), and curing duration (2–48 h). Mix design parameters comprised water-to-cement ratio (w/c: 0.35–0.55) and sample geometry (disc, prism). Derived thermodynamic features — CO₂ partial pressure, estimated Ca(OH)₂ availability from Bogue composition, and a dimensionless carbonation number (Nc = pCO₂ · t · D^-1, where D is an empirically calibrated diffusivity surrogate) — were computed a priori to provide mechanistically motivated covariates and reduce pure data-driven extrapolation. Four regression targets were measured per batch: CO₂ absorbed (wt.% of dry sample mass, thermogravimetric analysis), carbonation depth (mm, phenolphthalein spray on split cross-section), 28-day compressive strength (MPa, EN 12390-3), and porosity reduction (%, mercury intrusion porosimetry, MIP). All targets were verified for distributional consistency across the monitoring period; Kolmogorov–Smirnov tests detected no statistically significant seasonal drift (p > 0.12 for all targets), supporting the stationarity assumption during training.

Two-Stage Ensemble Architecture

Model development followed a sequential two-stage architecture designed to balance mechanistic fidelity with empirical flexibility.

• Stage 1: Physics-Informed Neural Network (PINN). A feedforward neural network was augmented with a soft physics constraint derived from the simplified one-dimensional carbonation diffusion-reaction equation: ∂C/∂t = D_eff · ∂²C/∂x² − k · C · [Ca(OH)₂] where C denotes dissolved CO₂ concentration, D_eff is effective diffusivity (parameterized as a function of w/c ratio and humidity via a learned sub-network), and k is a pseudo-first-order reaction rate constant. This PDE residual was evaluated at a set of interior collocation points and appended to the supervised loss as a weighted penalty term (λ = 0.1, selected via validation grid search). The network architecture consisted of five hidden layers (128–64–64–32–16 neurons), hyperbolic tangent activations, and four parallel output heads corresponding to the four targets. Multi-task learning was implemented with task-specific loss weighting calibrated by inverse training-set variance. Crucially, the PINN does not claim full mechanistic coverage; rather, it functions as a regularity constraint that penalizes predictions inconsistent with known diffusion physics, thereby reducing physically implausible extrapolations in sparse input regions.

• Stage 2: Gradient-Boosted Residual Correction. PINN residuals on the training fold were used as targets for an XGBoost ensemble, effectively performing structured error correction for system nonlinearities not captured by the simplified PDE (e.g., ettringite-related retardation, heterogeneous pore structure effects). This decomposition explicitly separates physics-grounded mean behavior from data-driven correction, preserving interpretability of each component.

Figure 1: Schematic of the Hybrid PINN+XGBoost Architecture for Predictive Carbonation Mapping, Combining Physics-Informed Constraints with Data-Driven Residual Correction

Training Protocol and Hyperparameter Optimization

The dataset was partitioned into training (80%, n = 8,198) and held-out test (20%, n = 2,049) sets using stratified temporal blocking to prevent data leakage across sequential batches. Model selection was conducted via five-fold cross-validation on the training partition. Hyperparameters for both the PINN (learning rate, dropout rate, physics penalty weight λ) and XGBoost (max depth, subsample ratio, column sample fraction, minimum child weight) were jointly optimized using Bayesian optimization with a Tree-structured Parzen Estimator (TPE, 200 evaluations), minimizing mean cross-validated RMSE across all four targets simultaneously. Early stopping (patience = 20 epochs) was applied during PINN training to mitigate overfitting.

Interpretability and Uncertainty Quantification

SHAP (SHapley Additive exPlanations) values were computed for the full ensemble using a background dataset of 500 randomly sampled training instances, enabling additive decomposition of predictions into per-feature contributions while respecting nonlinear interactions. Partial dependence plots (PDPs) were generated for the six highest-ranked SHAP features to visualize marginal response curves under the full covariate distribution, supporting process engineer interpretation. Critically, SHAP analysis was performed separately on Stage 1 and Stage 2 outputs to attribute variance to physics-governed versus empirically corrected components. Predictive uncertainty was quantified via Monte Carlo (MC) dropout at inference time (T = 100 forward passes, dropout rate p = 0.1), yielding per-prediction 90% credible intervals. Calibration of uncertainty estimates was assessed against held-out empirical coverage rates.

Real-Time Deployment Simulation and Baseline Comparisons

Deployment feasibility was evaluated by replaying twelve hours of synchronized sensor logs at 1 Hz through the trained ensemble, measuring end-to-end inference latency (target: < 500 ms per update) and memory footprint on a representative edge compute platform (Intel Core i7, 16 GB RAM, no GPU). Prediction stability under sensor noise was assessed by injecting Gaussian perturbations (σ = 2% of feature range). The proposed ensemble was benchmarked against four baselines: multiple linear regression (MLR), random forest (RF), standalone XGBoost, and a long short-term memory network (LSTM) applied to the 1 Hz time-series sensor stream within each curing batch. All baselines were trained on identical data partitions with equivalent hyperparameter search budgets. Performance was evaluated using RMSE, mean absolute percentage error (MAPE), and coefficient of determination (R²) on the held-out test set, reported with 95% bootstrap confidence intervals (B = 1,000 resamples).

Result

The hybrid physics-informed neural network with gradient-boosted residual correction (PINN+XGBoost) demonstrated strong predictive capability across all four target variables on the hold-out test set (n≈2,000 batches). Table 1 summarizes the performance metrics. The ensemble achieved R² values of 0.94 for CO₂ absorbed (% by mass), 0.91 for 28-day compressive strength, 0.89 for carbonation depth, and 0.87 for porosity reduction. These represent substantial improvements over the best-performing baseline (standalone XGBoost), which attained R² of 0.85, 0.82, 0.79, and 0.76 respectively. Root mean square error (RMSE) for CO₂ uptake was 1.2% absolute (versus 2.8% for XGBoost), corresponding to a mean absolute percentage error (MAPE) below 6% across the observed uptake range of 8–22 wt.%. Mean absolute errors remained low for mechanical properties (strength: 2.1 MPa; carbonation depth: 0.8 mm), well within acceptable industrial tolerances for process control.

               Table 1: Predictive Performance on Hold-Out Test Set (mean ± std. dev. from 5-fold CV)

Figure 2 presents parity plots for the four targets. Excellent agreement is observed between predicted and measured values along the 1:1 line, with minimal scatter even at high carbonation extents. Residual analysis revealed no systematic bias as a function of curing time or w/c ratio, confirming adequate capture of kinetic and stoichiometric effects.

Figure 2: Parity Plots for the Hybrid Model’s Predictions on the Hold-Out Test Set, Demonstrating R² Values of 0.94 (COâ?? uptake), 0.91 (strength), 0.89 (depth), and 0.87 (Porosity Reduction)

Benefit of Physics-Informed Constraints

The standalone PINN (without residual correction) already provided physically plausible predictions, reducing non-physical outputs by 67% compared to pure XGBoost. Instances of negative carbonation depths or porosity increases (thermodynamically inconsistent under the applied conditions) were largely eliminated. This improvement stems from the soft enforcement of the diffusion-reaction PDE, which constrains the model to respect mass conservation and reaction stoichiometry between CO₂ and calcium-bearing phases (primarily portlandite and, to a lesser extent, calcium silicates). When residuals were subsequently corrected by XGBoost, the hybrid retained most of this physical consistency while recovering the remaining variance attributable to unmodeled microstructural heterogeneities and minor phase interactions. Ablation studies showed that removal of the physics loss term (λ_p = 0) led to a 12–18% drop in R² for carbonation depth and porosity reduction on extrapolation test cases, underscoring the value of mechanistic grounding in low-data or out-of-distribution regimes typical of cement plant operations.

Feature Importance and Mechanistic Insights

SHAP analysis (Figure 3) identified partial pressure of CO₂ (pCO₂) as the dominant predictor (mean absolute SHAP contribution ≈33%), followed by curing temperature (22%) and w/c ratio (18%). These rankings align closely with established carbonation kinetics: higher CO₂ concentration increases the concentration gradient driving diffusion, elevated temperature accelerates both diffusion and the reaction rate constant k_r up to the optimum range (≈40–50°C), while lower w/c ratios reduce capillary porosity and thus effective diffusivity in a non-linear manner.

Figure 3: SHAP Analysis of Feature Importance, Highlighting pCO₂ (33%), Curing Temperature (22%), and w/c Ratio (18%) as Dominant Predictors of Carbonation Outcomes

Interestingly, raw meal MgO content emerged as the fourth most influential feature (≈9% contribution), particularly for CO₂ uptake and porosity reduction. This highlights the role of reactive magnesia in forming magnesium carbonates (e.g., nesquehonite or hydromagnesite) under humid conditions, contributing additional CO₂ sequestration capacity beyond calcium-based phases. Partial dependence plots (Figure 4) revealed a threshold effect around 1.5–2.0 wt.% MgO, beyond which marginal gains diminished— consistent with solubility limits and competition for reactive sites. Oxide ratios such as CaO/SiO₂ showed moderate importance, primarily modulating available portlandite after clinkering.

Figure 4: Partial Dependence Plots Illustrating Non-Linear Relationships between Key Input Features and CO₂ Uptake, with Threshold Effects for MgO Content

Local SHAP explanations for individual batches further enabled root-cause analysis. For under-performing batches, high SHAP values for humidity deviations explained reduced surface reaction rates due to pore water film effects. Such interpretability is critical for industrial adoption, allowing process engineers to translate model outputs into actionable adjustments rather than treating predictions as black-box recommendations.

Spatial Carbonation Mapping

The trained model was extended to generate high-resolution 2D carbonation maps across the pilot curing chamber volume (Figure 5). By incorporating spatial coordinates and local sensor-derived boundary conditions (gas flow patterns, wall temperatures), the PINN component solved the diffusion-reaction system at collocation points throughout the chamber geometry.

Figure 5: Spatial Carbonation Map Revealing 20% Lower CO₂ Uptake in Corner Zones Due to CO₂ Stratification, Enabling Targeted Chamber Redesign

Predicted maps revealed significant heterogeneity: corner and near-wall zones exhibited approximately 20% lower CO₂ uptake and shallower carbonation depths compared to central regions, attributable to CO₂ stratification and reduced convective mass transfer. These cold spots correlated with measured phenolphthalein fronts in validation samples. The model successfully identified optimal chamber loading configurations and baffle placements that could reduce spatial variance by an estimated 35%. Such mapping transforms traditional uniform curing assumptions into spatially resolved process optimization, directly supporting ultra-low emission targets through maximized CO₂ utilization efficiency.

Real-Time Inference and Uncertainty Quantification

In the digital twin simulation with 1 Hz sensor streaming, average inference time was 47 ms per batch on representative edge hardware, comfortably supporting closed-loop control at industrial timescales. Monte Carlo dropout yielded 90% confidence intervals with an average width of ±1.8% absolute CO₂ uptake, narrowing to ±0.9% under nominal conditions. These uncertainty bounds scaled appropriately with process deviation: wider intervals were produced for raw meal compositions with high leverage (Mahalanobis distance), providing a natural risk flag for operators.

Figure 6: Violin Plots of Uncertainty Quantification, Showing Epistemic and Aleatoric Components for Each Target, with a Mean 90% CI Width of ±1.8% for CO₂ Uptake

Propagation of uncertainty through the two-stage architecture showed that epistemic uncertainty dominated in early curing stages (<6 h), while aleatoric components increased with longer exposure due to microstructural variability. This decomposition enables tiered decision-making—e.g., continuing curing when upper-bound strength predictions meet specifications.

Outlier Detection and Process Diagnostics

The model demonstrated practical utility as an anomaly detector. Batches with prediction residuals exceeding 3× the median training residual were automatically flagged (≈4.2% of the test set). Post-hoc investigation traced most outliers to unlabeled raw meal variations, including undetected fly ash or slag adulteration that altered reactivity and available calcium. In one cluster of outliers, elevated Al₂O₃ content (detected retrospectively via SHAP) promoted formation of carboaluminate phases, reducing effective CO₂ uptake into calcite. Integration of the hybrid model with plant SCADA systems could therefore serve dual purposes: forward prediction and real-time quality assurance. Early flagging allows diversion of suspect batches to alternative curing regimes or corrective blending, minimizing waste and off-spec product.

Comparative Analysis and Limitations

Across all baselines, the hybrid model consistently outperformed alternatives, particularly in extrapolation scenarios (Figure 6). LSTM networks performed adequately on time-series subsets (R² ≈0.81 for CO₂ uptake) but struggled with static compositional features and lacked physical consistency. Traditional MLR exhibited poor handling of non-linear interactions, while random forest offered good accuracy but inferior uncertainty calibration

Figure 7: Radar Chart Comparing the Hybrid Model’s Performance (R², RMSE, MAPE, Latency) Against Baselines, Highlighting its Superiority in Accuracy and Real-Time Feasibility

Despite strong performance, limitations remain. The current PDE formulation assumes 1D-dominant diffusion and neglects full microstructural evolution (e.g., cracking or decalcification of C-S-H). Future extensions incorporating phase-field or lattice Boltzmann-informed constraints could further enhance fidelity. Additionally, while the 12-month dataset captured substantial seasonal variation, longer-term drift due to kiln feed changes requires continuous learning mechanisms. Overall, the results affirm that a mechanistically constrained hybrid AI approach can deliver accurate, interpretable, and deployable predictions for accelerated carbonation processes. By mapping carbonation performance in real time and space, the methodology provides a practical pathway toward optimizing ultra-low-emission cement manufacturing while maintaining product quality and process reliability.

Discussion

The results obtained in this study indicate that hybrid AI architectures combining physics-informed constraints with data-driven residual learning provide a viable pathway for predictive carbonation management in ultra-low-emission cement manufacturing facilities. The proposed framework demonstrated stable multi-output prediction capability across varying curing conditions while maintaining physically consistent responses under extrapolative operating regimes. From an industrial perspective, the principal contribution of the present work is not merely improved prediction accuracy but the integration of mechanistic interpretability, uncertainty awareness, and operational feasibility within a real-time carbonation control framework. A central finding is that the hybrid structure, composed of a physics-informed neural network (PINN) coupled with a residual gradient-boosting layer, substantially improves robustness relative to purely empirical machine learning approaches. The PINN component constrains predictions according to governing transport-reaction relationships associated with carbonation kinetics, including moisture-dependent diffusion and carbonate precipitation behavior. This constraint is particularly important under operational conditions poorly represented in the training data. For example, during simulated high-temperature curing scenarios approaching 50°C, conventional unconstrained neural networks produced physically inconsistent predictions, including unrealistically accelerated carbonation depths and nonmonotonic CO₂ uptake trends. In contrast, the PDE-constrained architecture maintained stable behavior because the solution space was bounded by mechanistically plausible transport dynamics.

At the same time, purely mechanistic models alone were insufficient to capture the full complexity of industrial carbonation chemistry. The residual gradient-boosting component played a critical role in learning nonlinear effects not explicitly represented in simplified governing equations, particularly those associated with metastable carbonate polymorph formation, SCM-specific reactivity variations, and transient pore-blocking phenomena. These effects are difficult to parameterize using first-principles formulations because they emerge from coupled microstructural evolution processes that remain only partially understood. The hybrid architecture therefore benefited from complementary strengths: mechanistic regularization prevented extrapolation failure, while data-driven residual correction captured unresolved chemistry and plant-specific operational variability. This finding supports broader evidence emerging in industrial AI literature that gray-box or hybrid modeling approaches may offer superior reliability for deployment in complex process industries compared with either purely mechanistic or purely black-box alternatives. The comparison with conventional plant control strategies further highlights the industrial relevance of predictive carbonation mapping. Existing carbonation curing operations within the studied facility rely primarily on empirical lookup tables derived from historical operating experience. These tables specify predefined curing durations, humidity windows, and pCO₂ targets based on generalized feedstock categories rather than real-time process state estimation. Although operationally straightforward, such approaches exhibit limited adaptability to dynamic process conditions. Simulation results in the present study showed that the baseline empirical strategy produced approximately 18% batch failure rates, defined as compressive strength values falling below specification thresholds. In contrast, AI-guided optimization reduced simulated failure rates to approximately 6% by dynamically adjusting curing duration, CO₂ flow distribution, and humidity control parameters according to predicted carbonation evolution

Figure 8: Flowchart of the AI-guided Closed-Loop Optimization Process, Integrating Real-Time Predictions with Dynamic Control of Curing Parameters

Importantly, these gains were not solely attributable to numerical optimization but also to improved process responsiveness under transient disturbances. The model demonstrated the ability to identify situations where increased CO₂ concentration would not improve carbonation efficiency due to excessive local pore saturation or premature carbonate densification. Under conventional rule-based control, such scenarios often lead to inefficient CO₂ usage and uneven curing performance. The predictive framework instead enabled adaptive balancing between transport-limited and reaction-limited regimes, thereby improving both process stability and material quality consistency. Another significant outcome of the study was the identification of substantial spatial heterogeneity within industrial carbonation chambers. The predictive carbonation maps revealed that fixed CO₂ injection through centralized manifold configurations produced persistent concentration gradients across the curing volume. Regions proximal to injection points experienced accelerated surface carbonation and early pore blockage, whereas distal regions exhibited delayed carbonation progression and reduced CO₂ uptake efficiency. These spatial disparities were not readily observable using conventional chamber-average measurements but became evident through high-resolution predictive mapping. The discovery has important implications for curing chamber design and process engineering. Current industrial configurations frequently assume relatively homogeneous gas distribution, yet the model results indicate that localized transport limitations can substantially reduce overall carbonation efficiency. The predictive framework therefore provides not only operational control recommendations but also insights for hardware redesign. Specifically, the results suggest that distributed manifold architectures, adaptive injection zoning, or dynamically controlled airflow routing may reduce concentration gradients and improve carbonation uniformity. Such findings illustrate how AI-driven process mapping can support plant-level engineering optimization beyond conventional parameter tuning alone.

Despite these promising outcomes, several limitations must be acknowledged. First, the model was trained using operational data derived from a single cement manufacturing facility characterized by a relatively narrow limestone chemistry envelope, with CaCO₃ contents ranging between approximately 88% and 92%. While this range is representative of many European clinker operations, mineralogical variability across global limestone deposits may significantly influence carbonation kinetics, pore evolution behavior, and carbonate precipitation pathways. Consequently, direct transferability of the trained model to facilities using substantially different raw materials cannot be assumed. Plants utilizing high-magnesium limestones, clay-rich feedstocks, or alternative SCM blends may require transfer learning adaptation or partial model retraining to maintain predictive reliability. This limitation reflects a broader challenge within industrial AI applications, where site-specific process signatures often constrain universal model deployment. A second limitation concerns the granularity of the input data. The current framework primarily utilizes batch-averaged chemical descriptors obtained from laboratory characterization and periodic online measurements. Although sufficient for pilot-scale deployment, this approach does not fully capture intra-batch variability or transient compositional fluctuations occurring during continuous operation. Future development should therefore prioritize integration of high-frequency per-sample sensing technologies, particularly near-infrared (NIR) spectroscopy capable of providing real-time mineralogical and moisture characterization directly within the process stream. The incorporation of continuous NIR chemistry data would likely improve short-term predictive responsiveness and enable finer-scale adaptive control strategies.

From an economic standpoint, the implications of improved carbonation efficiency are potentially substantial. For a representative cement plant processing approximately 0.5 Mt CO₂ annually, the model-predicted optimization corresponding to a 15% improvement in carbonation efficiency would increase annual CO₂ uptake by roughly 75 kt. Under prevailing European Union Emissions Trading System (EU ETS) carbon pricing scenarios, this additional sequestration capacity could translate to approximately €3–4 million in annual carbon credit value. Importantly, these estimates exclude secondary economic benefits associated with reduced batch rejection rates, shorter curing cycles, and improved energy utilization efficiency. Nevertheless, caution remains warranted because realized economic gains depend strongly on regulatory accounting frameworks, carbon credit verification methodologies, and operational implementation costs. Finally, although the present study focuses specifically on cement carbonation curing, the proposed AI architecture possesses broader applicability across related mineralization and curing systems. The hybrid predictive framework could potentially be adapted for autoclaved aerated concrete production, CO₂-cured recycled aggregates, alkali-activated materials, and mineralization-based direct air capture processes. In each case, the underlying challenge involves predicting coupled transport-reaction phenomena under dynamic industrial conditions using incomplete and noisy sensor data. The combination of mechanistic constraints with residual learning therefore represents a generalizable strategy for industrial decarbonization processes where purely empirical AI approaches may lack sufficient reliability for operational deployment.

Conclusion

This study presented a hybrid physics-informed machine learning framework for predictive carbonation mapping in ultra-low-emission cement manufacturing. The developed multi-output model simultaneously forecasts CO₂ absorption, carbonation depth, 28-day compressive strength, and porosity reduction under industrially relevant active carbonation curing conditions. By integrating a physics-informed neural network (PINN) embedding a diffusion-reaction PDE with XGBoost residual correction, the approach achieved R² values of 0.87–0.94 and mean absolute errors below 5% across all targets on the hold-out dataset. These results confirm the central hypothesis: a mechanistically constrained hybrid architecture can deliver sufficiently accurate predictions to support predictive process control in carbonation facilities, outperforming strong data-driven baselines while markedly reducing non-physical extrapolations. Four primary contributions are highlighted. First, to the authors’ knowledge, this constitutes the first multi-output predictive model tailored specifically for active carbonation curing at pilot scale, utilizing a rich dataset of over 10,000 batches with comprehensive raw meal, gas, and environmental features. Second, the two-stage PINN+XGBoost design effectively balances first-principles constraints with empirical flexibility, addressing a common limitation of purely black-box models in cement chemistry where thermodynamic and kinetic consistency is essential for trustworthiness. Third, the framework demonstrates real-time spatial carbonation mapping with quantified uncertainty (average 90% CI width ±1.8% CO₂ uptake and inference latency of 47 ms), enabling digital-twin-supported decision-making. Fourth, the model revealed substantial spatial heterogeneity within the curing chamber, particularly 20% lower uptake in corner zones due to COâ?? stratification as a previously under-appreciated optimization lever for maximizing sequestration efficiency without compromising strength development.

From a practical standpoint, the results open a clear pathway toward industrial deployment. The model can be integrated into existing distributed control systems (DCS) to dynamically adjust flue gas CO₂ flow rates, chamber temperature setpoints, and batch residence times in response to real-time sensor streams and raw meal variability. SHAP-derived insights further empower operators by translating predictions into actionable process adjustments, such as MgO-informed blending or humidity zoning. Uncertainty quantification provides the necessary safeguards for conservative control actions, mitigating risks inherent in cement production. Several avenues warrant further investigation. Closed-loop optimization via reinforcement learning could autonomously explore curing policies while respecting safety and quality constraints. Integration of life-cycle assessment (LCA) metrics into the objective function would allow explicit trade-off optimization between net CO₂ captured and energy penalties associated with heating or gas handling. A field trial at a 10 kt/year demonstration plant is planned to validate scalability, assess long¬term model drift, and quantify overall emission reductions under continuous operation. Beyond carbonation curing, the proposed hybrid modeling paradigm offers a transferable framework for any reactive material processing involving slow underlying physics and distributed phenomena. Analogous applications include hydrogen-based direct reduction of iron ore, hydrothermal processing of biomass, and controlled polymer curing, where embedding simplified governing equations can enhance generalization and interpretability. In summary, this work illustrates that carefully designed, physics-informed AI can accelerate the transition to low-carbon cement production by turning accelerated carbonation from an empirical art into a predictable, optimizable industrial process. While not a universal solution, the methodology provides a credible, deployable step toward maximizing CO₂ utilization while preserving product performance essential for the sustainable scaling of next-generation cementitious materials [1-17].

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