Machine Learning-Driven Prediction and Mechanistic Insight into CO ₂ Adsorption on Biomass-Derived Activated Carbons Using Explainable AI (XAI)

Abstract

To improve CO₂ uptake in Biomass-Derived Activated Carbon (BDAC), this study develops a multiscale hybrid digital twin framework. By integrating microscopic descriptors from Density Functional Theory and Molecular Dynamics (DFT/MD) with experimental data from 63 chemically diverse biomass precursors, a Gaussian Process Regression (GPR) model was developed using the Matérn 5/2 Automatic Relevance Determination (ARD) kernel. The framework achieved high internal training accuracy (R ² = 0.968) and Root Mean Square Error (RMSE = 0.2552), while providing a realistic generalization baseline across heterogeneous precursors with a 5-fold Cross-Validated (CV) R ² of 0.1567 and CV RMSE of 0.283. Explainable Artificial Intelligence (XAI) identified a synergistic mechanism for pore filling, revealing the interaction between ln Brunauer–Emmett–Teller (BET) specific surface area and ln total pore volume (ln S _BET × ln V _total) as the primary mechanical driver (rank 1). Sensitivity analysis identified a maximum thermal window near 400 °C, with 800 °C identified as the critical sintering threshold where structural breakdown begins. Furthermore, the model validates the nonreliance theory of raw material, demonstrating that the geometric surface properties exert a more dominant influence on performance than the biomass origin. The model was effectively stabilized by Bayesian optimization at a minimum internal training loss of 0.065, providing a scalable, materials information-based scheme for using high-resolution virtual screening to accelerate the circular carbon economy.

1. Introduction

1.1. Global Climate Imperatives and the Role of Biomass-Derived Activated Carbons (BDACs)

The growing concentration of CO₂ in the atmosphere, which is largely due to human activities, poses a serious threat to global climate stability, and therefore there is considerable interest in reliable Carbon Capture & Sequestration (CCS) technologies. , Adsorption with porous materials is one of the most studied CCS technologies. BDACs has been widely considered as excellent candidates for adsorbents owing to their various merits in the aspects of effective management and utilization of sustainable waste sources, low cost, the tailorability of surface characteristics. , It has come to attention that BDACs are a promising alternative to traditional CO₂ capture methodologies, which often suffer from high energy requirements and environmental issues. With the intrinsic difficulty in establishing the structure–property relationship between BDACs and their CO₂ adsorption performance, advanced modeling approaches are required to accelerate material design and optimization. The effect of factors such as pore size distribution, surface area, and adsorption condition are often cannot be illustrated effectively through the common prediction models of CO₂ adsorption capacity. , Therefore, to achieve accurate modeling and prediction of CO₂ adsorption behavior in porous carbonaceous materials, Machine Learning (ML) methods are used specifically, Extreme Gradient Boosting (XGBoost), Gradient Boosting Decision Trees (GBDTs), and Random Forests (RF). , These ML methods have excessive ability in capturing complex, nonlinear relationships between material properties and CO₂ capacity. These models are extremely useful for investigating complex material data sets because they can handle smaller data sets, reduce overfitting, and handle noisy or correlated characteristics. Furthermore, improving the transparency and accuracy of predictions requires the integration of XAI methodologies with ML models. XAI techniques efficiently convert black-box models into more comprehensible white-box models by providing insights into the critical elements controlling CO₂ adsorption. XAI can direct the synthesis and modification of BDACs to maximize CO₂ capture efficiency by determining the most important variables, such as ultramicropore volume and surface area. This approach enables a more rational design process, going beyond experimental trial-and-error methods to a more comprehensive and objective analysis, which can be applied to a wider range of porous carbon materials. According to standard scientific assessments, ML and BDACs are increasingly being used to collect CO₂. This work aims to provide a reliable and easy-to-understand ML framework used to predict CO₂ uptake on porous carbon composites, leveraging the advantages of XAI and tree-based models. The main objectives to be achieved by integrating state-of-the-art ML methods with a highly curated, specialized data set of porous BDACs’ properties are as follows:

• Develop a physically grounded prediction model for the CO₂ adsorption capacity of porous BDACs.

• Identify the key multiscale synergistic interactions that regulate CO₂ uptake using XAI approaches.

• Explain the fundamental processes by which CO₂ is adsorbed by porous BDACs by reconciling macroscopic textures with atomistic signatures.

• Provide a comprehensive and objective process for developing and improving porous BDACs for effective CO₂ adsorption.

The development of sustainable and affordable carbon capture technologies will accelerate dramatically if ML and XAI technologies are successfully integrated into organic waste treatment research. This would support global efforts to reduce the effects of climate change and promote a circular economy. This approach encourages sustainable waste management while simultaneously reducing CO₂ emissions using biomass waste. The present study establishes a robust ML framework for predicting CO₂ uptake that remains effective within the specialized chemical space of BDACs. While the data set is focused, the integration of multiscale, DFT-derived descriptors enables the framework to capture fundamental interactions that are physically transferable across similar porous matrices, providing a scalable proof-of-concept for targeted material design.

1.2. Current Landscape of ML in CO₂ Adsorption on BDAC

1.2.1. Overview of Established ML Models and Their Typical Applications

The application of ML to the study of CO₂ adsorption, especially with regard to BDAC, is widely documented. , Predictive modeling and optimization problems often involve a range of supervised ML methods. These include tree-based ensemble models as Extra Trees Regressor, XGBoost, Light Gradient Boosting Machine (LGBM), Categorical Boosting (CatBoost), Adaptive Boosting (AdaBoost), RF, Gradient Boosting Regressor (GBR), Decision Tree (DT), and GBDT. Furthermore, neural networks (Artificial Neural Networks (ANN), Radial Basis Function-Neural Networks (RBF-NN)) and Support Vector Machine (SVM) are frequently used. , To interpret these, methodology like SHapley Additive explanations (SHAP) is applied. These models are used mainly to make predictions of CO₂ adsorption capacity based on a variety of material characteristics and operating conditions. Furthermore, they support optimization and reduce the need for trial-and-error in the development of novel materials by directing experimental synthesis to achieve desired material characteristics or maximize adsorption performance. The following error functions are used to investigate the accurate performance of these models including; Coefficient of Determination (R ²), RMSE, and Mean Absolute Error (MAE). ,

1.3. Analysis of Key Material Properties and Synthesis Parameters as ML Descriptors for CO₂ Uptake

Biomass source, pyrolysis/carbonization temperature, V _total, S _BET, activation type, activation agent and activation temperature factors were included in the data set inputs for accurate prediction of the CO₂ adsorption behavior on activated carbon materials.

Textural Features: It has been repeatedly demonstrated that ln V _total, and ln S _BET particularly the characteristics of micropores and ultramicropores have a significant impact on CO₂ adsorption capacity. These fine pores produce strong confining effects and increased van der Waals forces, both of which are necessary for physical adsorption. ,

Synthesis criteria: The type of biomass feedstock, pyrolysis/carbonization temperature, activation temperature, and activation method (chemical or physical), and the activating agent used greatly influence the chemical composition of the activated carbon surface and its final surface properties. For example, carbon is preferred to be chemically activated rather than physically activated. Chemical processes typically produce materials with better surface quality and higher porosity, which explains this preference. In addition, the chemical activation process is more energy efficient, operating at lower temperatures than its physical counterpart. The choice of activating agent (such as potassium hydroxide (KOH), phosphoric acid (H₃PO₄), zinc chloride (ZnCl₂)) affects the development of surface area and pore structure. ,

Fixed Operating Conditions (25 °C and 1 atm): The adsorption of CO₂ using BDACs for each sample in the data set has been performed at fixed ambient operating conditions of temperature = 25 °C and pressure of 1 atm. The fixed conditions in this data set enable a deeper, more focused investigation into the intrinsic material properties and synthesis parameters that dictate CO₂ uptake at these particular, industrially relevant conditions, whereas many studies vary temperature and pressure as inputs to optimize adsorption conditions. Because of this limitation, research is now more focused on improving material synthesis and design than the actual adsorption process.

Table provides a brief overview of the current uses of ML to CO₂ adsorption using BDAC, including common input descriptors, output targets, and reported results. This provides context for the data set and highlights areas that could benefit from further investigation.

1. State-of-the-Art ML Models and Key Descriptors for CO₂ Adsorption on BDAC.

ML Model(s) Used	Key Input Descriptors (Examples)	Output Target	Performance Metrics (Typical R 2)	Relevant Operating Conditions (T, P)	Refs
GBDT, LGBM, XGBoost	Textural properties, compositional features, adsorption T & P	CO2 uptake capacity	R 2 > 0.84 (test), > 0.98 (train)	Varied T and P (general application)
RF, ANN, SVM, XGBoost, RBF-NN	Operating conditions (T, P), textural properties (surface area, pore volume), chemical composition	CO2 uptake capacity, CO2 solubility	R 2 > 0.9 (often >0.99 for train)	Varied T and P (general application)
SHAP + RF	S BET, micropore/mesopore volumes, C/H/O/N wt %, T, P	CO2 uptake capacity	High accuracy (R 2 not specified)	Specific T (298 K), low P (general)
RF, GBR, DT, ANN, SVM	Feedstock composition, activation parameters (T, time, heating rate), activating agent ratio, particle size	S BET, V total	R 2 > 0.96	Synthesis conditions, not adsorption T/P
RF	Pore structure, chemical properties, adsorption conditions	CO2 uptake capacity	R 2 > 0.97 (train and test)	Varied P (0–1 bar), unspecified T
GBDT, XGBoost, LGBM, RF, Catboost, Adaboost	Adsorbent properties, adsorption conditions (T, P)	CO2 uptake capacity	GBDT outperformed (accurate prediction)	Varied T and P (general application)

1.4. Research Gaps

Although current ML applications of CO₂ adsorption on BDAC show high predictive accuracy (R ² > 0.95 in controlled experiments), a significant research gap remains regarding the transparency of the mechanism and generalizability across different feedstocks. , Most existing models remain vague, often overfitting to certain types of biomass or limited laboratory conditions. , Given the specialized nature of these materials, high-fidelity modeling requires more than just statistical correlation. While this study achieves a high training fit (R ² = 0.968), it moves beyond simple curve-fitting by prioritizing predictive reliability through an integrated multiscale approach. XAI was utilized to decode the black-box nature of tree-based models, identifying the specific pore structures and surface characteristics that drive CO₂ uptake. These data-driven findings are then cross-validated through atomistic DFT-MD simulations to provide a robust physical basis for the model’s logic, bridging the gap between laboratory observation and fundamental theory.

1.4.1. Beyond Predictive Accuracy: Toward Mechanistic Understanding and Causal Inference

1.4.1.1. The Black-Box Challenge and the Need for XAI

The direct use of XAI algorithms on the BDAC data set is an important aspect of this study. SHAP analysis is used to determine the discriminating effect of each input characteristic, from the biomass source to the activation temperature, rather than viewing ML as a black box for prediction. These techniques were applied to the selected data set under constant adsorption conditions (25 °C and 1 atm) to identify and rank the basic physical properties affecting CO₂ adsorption. This approach enables us to determine the exact effect of ultrafine pore size and specific surface area on adsorption efficiency. Driven by a shift from feasibility study to applied explanation, mere correlation can now be gone beyond, and an accurate, model-based explanation can be provided for why some synthesis pathways are superior to others.

1.4.2. Integrating ML with Atomistic Simulations (DFT/MD) for Deeper, Fundamental Insights

The insights obtained by macroscopic ML models are frequently restricted to the size of the input features (e.g., S _BET, V _total), even with XAI. Atomic and molecular insights are essential to comprehending the fundamental mechanics of CO₂ adsorption. This basic knowledge of adsorbate–adsorbent interactions, pore-level diffusion, and the precise function of functional groups is frequently lacking in conventional experimental techniques and macroscopic ML models. MD simulation and DFT are powerful computational techniques that allow a very accurate understanding of these processes at the molecular level. , It shows how CO₂ molecules interact with specific pore shapes, bind to different surface functional groups, and diffuse throughout the carbon matrix. Due to their high computational cost, these simulations can only be used in large-scale examination of materials or in comprehensive parametric studies. In this work, coupling ML/XAI with DFT-MD simulations bridge the gap between macroscopic descriptors and molecular interactions. Rather than using simulations in isolation, XAI-identified critical features is used to parametrize the atomistic models. This facilitates explanation at the molecular level, why specific activation types or surface functional groups highlighted by the ML model enhance physical or chemical adsorption. The constant temperature and pressure (25 °C, 1 atm) in the data set are ideal in such a comprehensive atomic simulation, because they eliminate the complexity of variable thermodynamic effects on molecular interactions, allowing a focused study of the interactions of matter with CO₂. A predictive model is trained using the data set’s experimental data in an integrated approach that combines ML, XAI, and DFT/MD. The XAI is used to identify important macroscopic properties (such as specific V _total ranges and activation types) that influence CO₂ uptake. Next, the atomic-level reasons for the importance of this property at 25 °C and 1 atm can be explained by simulating DFT/MD enhanced by ML. For example, this may show how specific surface chemical properties (affected by type of activation, and biomass source) or pore geometry (derived from pore size and BET data) can enhance the physical or chemical adsorption of CO₂ at ambient conditions. This multiscale method makes a highly innovative contribution by providing fundamental insight beyond empirical correlations.

1.4.3. Addressing Data Heterogeneity and Model Generalizability

1.4.3.1. Quantifying and Managing Uncertainty (UQ) in ML Predictions

Both experimental data and ML algorithms are inherently uncertain. Natural biomass composition fluctuation, small variations in synthesis conditions, and measurement errors during material characterization are examples of sources of UQ in the context of CO₂ adsorption. For example, the biochemical makeup of biomass sources varies greatly, which directly affects the characteristics of the activated carbon that is produced. A high-impact study would quantify the forecast’s reliability by providing a prediction interval or confidence boundaries in addition to a single CO₂ uptake number. This entails differentiating between epistemic UQ (UQ resulting from model limitations or inadequate data) and aleatoric UQ (inherent variability in the data itself). For this reason, ensemble methods with UQ estimates (such as bootstrapping in RFs) or Bayesian ML methodologies are appropriate. Less research has been done on the methodical use of UQ quantification to account for biomass variability in activated carbon synthesis for CO₂ adsorption. The reliability and usefulness of the ML model for practical application and well-informed decision-making in industrial contexts are greatly increased when quantified UQ is included with forecasts.

1.4.4. Developing Robust ML Models for Out-of-Distribution (OOD) Generalization and Transfer Learning

The capacity of models to generalize well to OOD samples materials or situations that differ significantly from those encountered during the model’s training phase is a major difficulty in applying ML to materials science. An example of an OOD difficulty is biomass source variability, where a model trained on one type of biomass may perform badly on a new, untested biomass source. Broad application requires models that are resilient to these kinds of fluctuations. Research can concentrate on creating ML models with robust OOD generalization capabilities to address this. The flexibility of models can be enhanced using methods such as transfer learning, which applies knowledge from a particular task or field (such as activated carbon from a particular biomass source) to another similar task (such as activated carbon from a different biomass source). Cutting-edge technologies, including competitive learning to generalize goal-oriented design models, may improve the ability of models to adapt to unexpected changes in biomass types or synthesis conditions. , Developing models that work efficiently on unknown biomass sources or under dramatically changing synthesis conditions is one of the most difficult tasks in materials science. Overcoming this barrier is critical to commercial growth and the widespread application of activated carbon produced from biomass in CO₂ capture, making it a critical research and innovation topic.

1.5. The Present Study: A Hybrid ML/XAI/DFT-MD Framework

This study contributes a three-tiered hybrid framework designed to move beyond black-box predictions:

Level 1 (Macro-Scale): Level 1 (Macro-Scale): GPR, XGBoost, RF, and GBDT are used to predict CO₂ uptake across diverse biomass feedstocks.

Level 2 (Interpretability): SHAP analysis is applied to rank descriptor importance, identifying the critical thresholds.

Level 3 (Atomistic-Scale): DFT and MD simulations are performed on the top-performing configurations identified by Level 2 to elucidate the binding energies and MD patterns that drive performance. This integrated methodology ensures that findings of this study are both statistically robust and physically grounded.

2. Materials and Methods

2.1. Data Set Acquisition and Preprocessing

The experimental CO₂ adsorption capabilities of different BDACs, produced using a variety of bioraw materials and synthesis methods, constitute the data set used in this work. The input properties include basic synthesis parameters and structural parameters, such as biomass source, pyrolysis/carbonization temperature, S _BET, V _total, activation type, activation agent, and activation temperature as represented in (Table 1S). A comprehensive properties engineering methodology was used to ensure good model performance and deal with the nonlinear and twisted nature of the material properties data. Both the response variable (CO₂ adsorption capacity) and important predictive factors of the structure were converted using logarithmic transformation according to the method described in (eq ) in order to stabilize the variance and reduce the effect of anomalous values. Change the variable used for prediction (eq ):

$${\mathit{y}}^{\prime }=\ln (\mathrm{capacity}+1)$$ 1

where y′: The transformed CO₂ adsorption capacity (the target the model tries to predict). Capacity: The raw experimental value (in mmol/g). The (+1): This is a mathematical safety measure. Since the natural log of zero is undefined (ln(0) = −∞), adding 1 ensures that even if a sample has zero or near-zero adsorption, the result is a real number (ln(1) = 0).

$${\mathit{x}}_{\mathit{i}}^{\prime }=\ln (1+{\mathit{x}}_{\mathit{i}})$$ 2

where x′ _i : The transformed input feature (like S _BET or V _total). x_i : The raw physical property.

To illustrate the complementary effects of ln S _BET and ln V _total, reaction boundaries (ln S _BET × ln V _total) and polynomial properties (ln S _BET)² were added to the prediction matrix. These derived parameters allow the model to explain the complex relationship between the available S _BET and the available V _total.

2.2. Data Diversity and Biomass Precursor Classification

The data set that forms the basis of the forecasting framework is characterized by the diversity of raw materials and their chemical multidimensionality. The data set was classified according to the structural ratios of lignocellulosic materials to improve the model’s understanding of the complex CO₂ adsorption environment; Agricultural crop stems and casings are rich sources of cellulose precursors. Because their glucose units are linearly controlled, these materials typically provide a wide surface area for carbon. Fruit seeds, wood chips, and nut shells are examples of lignin-rich raw materials. The cross-linked phenolic structure of lignin encourages the formation of very fine holes. By including these distinct chemical properties, the framework is designed to monitor broader trends in waste-to-energy conversion. While the extreme variability of these 63 separate sources naturally limits global R ² metrics, this classification ensures that the internal logic of the model is based on the basic biochemical building blocks of biomass rather than a single homogeneous waste stream.

2.3. Fundamental Adsorption Theory and Pore-Filling Mechanism

Adsorption of CO₂ onto BDAC is a multiscale physical phenomenon that is primarily subject to physical adsorption. At ambient conditions (25 °C, 1 atm), the interaction between the quadrupole CO₂ molecules and the carbon surface is driven by London scattering forces and electrostatic interactions.

2.3.1. The Role of Microporosity and the Dubinin–Radushkevich Theory

In contrast to high-pressure adsorption that follows the single-layer Langmuir model, the process of ambient CO₂ capture on BDACs is best described by pore filling theory. In ultrafine pores, adsorption efforts from opposite pore walls overlap, creating a deep potential well that greatly enhances the attraction of gas molecules. This is mathematically represented by the Dubinin–Radushkevich (DR) (eq ):

$$\mathit{W}={\mathit{W}}_{\mathrm{o}}{\mathrm{e}}^{[-{(\frac{\mathit{A}}{{\beta \mathit{E}}_{\mathrm{o}}})}^2]}$$ 3

where the Adsorption Potential (A) is defined by the Gibbs free energy of adsorption. It is calculated from the following (eq ):

$$\mathit{A}=\mathit{RT}\ln \frac{{\mathit{P}}_{\mathrm{o}}}{\mathit{P}}$$ 4

where W (cm³/g): The volume of the adsorption space filled by the condensed CO₂ at a given temperature and pressure. W _o (cm³/g): The limiting volume of the adsorption space, representing the total micropore capacity. In this ML model, this is the physical equivalent of the feature V _total. E _o (kJ/mol): The characteristic energy of adsorption, which reflects the structural heterogeneity of the carbon pores. β (Dimensionless): The affinity coefficient, which is a scaling factor for the polarizability of CO₂ relative to a reference gas (usually benzene, where β = 1). For CO₂, β ≈ 0.35. R (8.314 J/mol K): The universal gas constant. T (K): The temperature in Kelvin.

In this hybrid multiscale framework, E _o is no longer treated as a static constant but is augmented by DFT-calculated binding energies. As demonstrated by the Partial Dependence Plot (PDP) (Figure b), the characteristic energy of the carbon matrix exhibits a nonlinear sensitivity to electronic-scale affinities, which explains the high relevance of atomistic descriptors in the final GPR model.

9.

Parity plot of experimental vs predicted CO₂ adsorption capacity for the GPR model (Training Fit, R ² = 0.968).

2.4. ML Algorithmic Architecture

To guarantee the reliability of the results, two classes of algorithms were evaluated, culminating in the development of a physically informed digital twin:

• Ensemble Trees (RF/XGBoost): These models were utilized to capture high-dimensional interactions between macroscopic synthesis parameters.

• GPR: A nonparametric Bayesian method was chosen as the basic structure of the hybrid framework. A special advantage of GPR is the use of ARD. The model successfully separated the physical effect of atomic properties from experimental noise by converging on an exponential kernel to determine automatic significance.

2.5. Bayesian Hyper-Parameter Optimization and Multiscale Training

The Expected Improvement (EI) acquisition function was used in Bayesian optimization to prevent overfitting. In this iterative process, a set of hyper-parameters for optimal kernel metrics and noise bounds were processed. The use of a minimum (σ = 0.0001) significantly improved the training stability. This limitation ensures that the model provides a reliable quantitative measure of UQ. It was detected during a 50-repeat optimization cycle (Figure b). Even when biomass waste streams are projected OOD, the digital twin maintains a high degree of generalization by distinguishing between experimental measurement noise (randomness) and model’s UQ (cognitive). K-type cross-validation (k = 5 for the integrated model) was used to ensure that performance measures, specifically the CV RMSE of 0.283, reflect the model’s ability to predict the properties of materials that have not yet been physically manufactured.

10.

Bayesian optimization of the digital twin­(a) 3D objective function landscape identifying the optimal hyperparameter region (Standardization: True; σ ≈ 10^–4) where model loss is minimized. (b) Optimization trajectory showing stepwise convergence of ln­(1 + Training Loss) to a global minimum of 0.065. The rapid stabilization validates the efficiency of the GPR-ARD framework in reconciling multiscale descriptors.

2.6. Mathematical Architecture of the XAI Framework

To ensure transparency to the Ensemble Trees model, SHAP was used based on alliance game theory. The goal is to distribute the final prediction of CO₂ adsorption among input features such as S _BET and V _total.

2.6.1. The SHAP Value Equation and Feature Attribution

To quantify the individual contribution of each synthesis and textural parameter to the final CO₂ adsorption prediction, SHAP method is used. This method is based on coalitional game theory, where the final prediction is considered a payout and each input feature is a player. The SHAP value (Φ _i ) for a specific feature i is defined as represented in (eq ):

$${\Phi }_{\mathit{i}}(\mathit{f},\mathit{x})=\sum _{\mathit{S}\subseteq \mathit{N}\backslash (\mathit{i})}\frac{|\mathit{S}|!(\mathit{n}-|\mathit{S}|-1)!}{\mathit{n}!}[\mathit{f}(\mathit{S}\cup \{\mathit{i}\})-\mathit{f}(\mathit{S})]$$ 5

where Φ _i : The SHAP value (attribution) for feature i. A positive Φ _i indicates the feature increased the CO₂ uptake prediction relative to the average, while a negative value indicates a decrease. n: The total number of input features in the model (e.g., temperature, S _BET, V _total, etc.). S: A subset (coalition) of features that does not include the feature i. |S|: The number of features currently in the subset S. f(S ∪ {i}): The model’s prediction of CO₂ uptake when feature i is included in the set of predictors. f(S): The model’s prediction of CO₂ uptake based only on the subset S, excluding feature i. [f(S ∪ {i}) – f(S)]: The marginal contribution of feature i. This represents how much the CO₂ capacity changes specifically because of that one property. $\frac{|S|!(n-|S|-1)!}{n!}$ : The weighting factor.

To ensure the identified feature attributions were not biased by specific biomass outliers in the data set (N = 63), SHAP values were aggregated across the CV iterations. This approach confirms that the global importance of descriptors specifically the synergy between ln S _BET and ln V _total remains stable regardless of which specific biomass sample is excluded from the training set. This stability validates that the model is capturing universal structural drivers rather than overfitting to individual feedstock characteristics.

2.7. Performance Evaluation Metrics

Three main statistical variables were used to measure the accuracy of the resulting models’ predictions and their ability to generalize accurately.

2.7.1. Coefficient of Determination (R ²)

The R ² represents the ratio of the variation in CO₂ adsorption capacity that can be predicted by independent input properties (e.g., S _BET and pyrolysis/carbonization temperature). It can be calculated from (eq ): ,

$${\mathit{R}}^2=1-\frac{\sum _{\mathit{i}=1}^{\mathit{n}}{({\mathit{y}}_{\mathrm{predicted}}-y_{\mathrm{actual}})}^2}{\sum _{\mathit{i}=1}^{\mathit{n}}{({\mathit{y}}_{\mathrm{predicted}}-y_{\mathrm{mean}})}^2}$$ 6

2.7.2. Root Mean Square Error (RMSE)

RMSE provides a measure of the average magnitude of the error between the predicted values (ŷ _i ) and the actual observed values (y_i ), expressed in the same units as the CO₂ uptake (mmol/g). It can be calculated from (eq ): ,

$$\mathrm{RMSE}=\sqrt{\left(\frac{1}{\mathit{n}}\right)\sum _{\mathit{i}=1}^n{({\mathit{y}}_{\mathit{i}}-{ŷ}_{\mathit{i}})}^2}$$ 7

RMSE is quite sensitive to extreme outliers since it squares errors before averaging. Even when predicting extremely complex and challenging samples like diverse biowaste streams, the model did not encounter large mistakes, as evidenced by its low CV RMSE of 0.283.

2.7.3. Mean Absolute Error (MAE)

MAE calculates the average absolute difference between experimental and predicted values, providing a linear score that represents the typical distance of a prediction from the actual that can be calculated from (eq ): ,

$$\mathrm{MAE}=\left(\frac{1}{\mathit{n}}\right)\sum _{\mathit{i}=1}^{\mathit{n}}|{\mathit{y}}_{\mathit{i}}-{\mathit{ŷ}}_{\mathrm{i}}|$$ 8

MAE does not penalize huge errors as severely as RMSE does. A standard diagnosis in scientific articles is to compare CV MAE (0.218) to CV RMSE (0.283). , Because these values are remarkably close, this suggests that the error distribution in this study is small and entirely free of substantial extreme outliers.

2.8. Model Validation and Robustness

Given the specialized nature of BDAC data sets (N = 63), a rigorous CV strategy was employed to mitigate the risk of overfitting. Unlike a standard 80/20 split, which can lead to high variance on small data sets, this approach ensures that the reported R ² and RMSE reflect the model’s ability to generalize to unseen feedstock categories. Furthermore, feature pruning was utilized to maintain a high observations-to-features ratio, ensuring model complexity was commensurate with the data set size. To ensure mechanistic drivers were not artifacts of the small sample size, a feature stability analysis was performed. As shown in Figure , the trained ARD hyper-parameter weights for key descriptors including multiscale features such as ln S _BET, ln V _total, and atomistic DFT/MD signatures remained consistently stable across 63 random subsampling iterations. This confirms the robustness of the physical signals captured by the model and demonstrates that the integration of atomistic-scale data provides stable, predictive power despite the data set constraints (N = 63).

1.

Feature stability and sensitivity analysis showing the tight distribution of trained hyper-parameter weights across random subsampling iterations (N = 63).

3. Results and Discussion

3.1. Statistical Analysis of the Curated Data Set

A detailed statistical analysis was implemented for the data set of the BDACs adsorbents before the training of the model. The variety of biomass precursors and chemical activation agents is reflected in the wide numerical range of key surface characteristics. To address the distribution of the target variable, the CO₂ adsorption capacity was processed using ln­(1 + Outcome). This approach ensures that the model remains sensitive to variations across different scales of adsorption performance.

3.2. Evaluation of Predictive Performance and Model Benchmarking

The performance of the three intelligent models Ensemble (RF/Bagged Trees), GPR, and SVM was benchmarked using 5-fold CV to ensure generalizability.

As shown in Table , a significant discrepancy was observed between the high internal training accuracy (R ² = 0.968 for the GPR model) as shown in Figure and the test accuracy after CV (R ² = 0.1567). While this variability usually indicates model overfitting, in the context of this study, it directly reflects the extreme chemical and structural variability among 63 unique biomass precursors. Because CV folds force models to evaluate completely OOD biomass classes, CV R ² value of 0.1567 represents a very conservative lower bound for prediction. This is visually evident in the CV parity plot (Figure ), where the predictions of the GPR model closely cluster around the basic statistical average of 1.5282 (which corresponds to an average physical capacity of CO₂ of 3.7906 mmol/g). Importantly, although tracking linear trends across highly diverse raw materials is poor, the CV RMSE value remains low at 0.283. This confirms that the model maintains narrow and reliable error limits, making it a reliable numerical tool for basic engineering examinations without showing extreme predictive failures on unfamiliar biomass flows.

2. Statistical Performance Metrics for Internal 5-Fold CV of CO₂ Adsorption Capacity Prediction Models.

Model Architecture	Internal R 2 (Training)	CV R 2 (Test)	Internal RMSE (Training)	CV RMSE (Test)	Internal MAE (Training)	CV MAE (Test)	Rank
GPR	0.968	0.1567	0.2552	0.283	0.198	0.218	1
SVM	0.964	0.1210	0.2579	0.289	0.201	0.223	2
Ensemble (RF/Bagged Trees)	0.941	0.0850	0.2788	0.295	0.224	0.227	3

2.

GPR Model Internal Fit Analysis: Predicted vs Actual ln­(1 + Outcome) values.

4.

CV parity plot demonstrating model generalization across diverse biomass categories (CV R ² = 0.1567).

3.3. Global Feature Importance and Parameter Rankings

To address the complexity of the high-performance GPR digital twin, a Global Permutation Feature Importance approach was used to identify the primary drivers of CO₂ adsorption. By quantifying the increase in MSE when permuting individual predictors, this methodology provides a rigorous mathematical basis for variable significance, as illustrated in Figure .

3.

Global feature importance metrics demonstrating the relative impact of processing parameters and multiscale descriptors based on permutation-induced increase in MSE.

Analysis of the importance of general properties showed that the reaction coefficient (ln S _BET × ln V _total) had the greatest influence on the model’s predictions, explaining the highest increase in MSE. This demonstrates a fundamental synergistic relationship: while an increase in ln S _BET provides the necessary binding sites, its effects are physically limited unless offset by an increase in ln V _total to serve as a storage vessel. This result is fully consistent with the well-known pore filling theory. Furthermore, the high importance of activation type (rank 2) compared to biomass source (rank 5) provides experimental evidence supporting the neutral theory of raw materials. This suggests that the final carbon structure is more influenced by chemical activation mechanisms than by the chemical composition of the raw material. Finally, the pyrolysis temperature is the primary thermodynamic driver, determining the initial structural composition of biochar prior to chemical activation. To accurately evaluate the performance of the GPR on the N = 63 data set, multiscale cross-verification using an improved feature set was used. As shown in Figure , integrated validation achieved CV R ² value of 0.1567, representing a realistic lower bound for predicting biomass classes outside the distribution range. This model is based on a calculated base value of 1.5282, which corresponds to the average physical CO₂ absorption capacity of the data set of 3.7906 mmol/g. To address the potential over conciliation problem and verify these results, a stability analysis was performed (Figure ), which confirmed that the importance of the interaction between ln S _BET and ln V _total remains statistically stable (p < 0.05) across multiple subsets of random data, even when global predictive variance is high.

The adsorption mechanisms at 25 °C and 1 atm are illustrated by the model classifications and performance measures given in Tables and . Using a characteristic threshold that differentiates between the main motor drives, the Pareto chart (Figure ) shows the overall relative importance of each input characteristic. At the expense of criteria specific to raw materials (rank 5) and thermal conditions (rank 7 to 10), the GPR prioritized surface properties and their interactions (rank 1 to 4). According to this hierarchy, the chemical process that leads to pore formation is more important for the adsorption of CO₂ from the specific biomass source into the waste stream. The remarkable synergy of (ln S _BET × ln V _total) has confirmed that physical adsorption is the main mechanism.

3. XAI Analysis of Global Feature Importance and Mechanistic Drivers.

Rank	Feature Descriptor	Relative Importance	Physical Significance
1	ln S BET × ln V total	0.45	Synergistic interaction governing pore-filling capacity
2	Activation Type	0.42	Chemical mechanism of pore creation
3	ln S BET	0.38	Primary surface area availability
4	ln V total	0.35	Logarithmic scaling of pore capacity
5	Biomass Source	0.34	Inherent precursor chemistry
6	(ln S BET)2	0.29	Nonlinear area dependence
7	Activation Agent	0.14	Specific chemical reactant influence
8	Carbonization Process Type	0.1	Initial thermal treatment method
9	Pyrolysis/Carbonization Temp (°C)	0.08	Thermodynamic drive for carbonization
10	Activation Temp (°C)	0.06	Thermal energy for secondary porosity

5.

Global feature importance Pareto chart for the GPR model.

3.4. Mechanistic Insights via SHAP Analysis: Physical Chemistry of CO₂ Adsorption on BDACs

To complement the global framework, local interpretability was conducted exclusively via SHAP analysis to decipher sample-specific behavior (Figure ). In Figure , the horizontal bars show how much each attribute deviates from the model’s prediction from the base value of the data set ln­(1 + Outcome) = 1.5282 (which represents an average physical adsorption capacity of 3.7906 mmol/g). This basis provides a realistic benchmark for evaluating the performance of biomass precursors or activators, whether above or below the data set average. The most significant positive contributions arise from ln V _total and the synergistic interaction term, which enhances the predominance of pore filling. In contrast, the small contribution of the biomass source supports the neutral theory, suggesting that the engineered thermochemical properties influence the underlying chemical properties of the feedstock. It should be noted that the negative SHAP value for the activation type in this representative sample shows how some chemical pathways can limit adsorption capacity locally despite their great global importance. With a characteristic CV RMSE value of 0.283, the GPR model serves as a reliable digital twin, providing a solid foundation for industrial-scale screening without the need for extensive laboratory characterization.

6.

Local interpretability via SHAP analysis for a representative BDAC sample.

3.5. Parametric Sensitivity and Material Optimization

Partial Dependence Plot (PDP) and SHAP value distributions illustrate the sensitivity of predicted CO₂ adsorption capacities to specific compositional and structural properties. By isolating the influence of primary drivers, such as the (ln S _BET × ln V _total) interaction (Rank 1), while maintaining other parameters at their data set averages, this analysis provides a direct trajectory for material optimization. These results demonstrate how adsorption evolves nonlinearly with structural maturation, providing robust computational support for pore-filling theory.

3.5.1. The Trade-Off between Temperature and Porosity

The sensitivity of the GPR model to synthesis conditions is demonstrated by the correlation between carbonization/pyrolysis temperature and CO₂ adsorption. As shown in the PDP (Figure ), the model defines an ideal thermal range centered around 400 °C within the chemical range of the raw materials under study. Volatile materials remain that clog potential pore networks, and incomplete carbonization occurs at temperatures well below this limit. On the other hand, a steady decrease in the CO₂ capacity is observed after exceeding 400 °C. The model concludes that 800 °C is a critical temperature at which sintering effects begin to overcome pore formation. At these high temperatures, carbon sheet fusion can cause very fine pores to collapse into larger, less efficient structures, reducing the effective CO₂ adsorption capacity. Although the carbonization temperature ranks ninth in fundamental importance globally (Table ), it serves as the critical thermodynamic guardian of subsequent activation success.

7.

PDP of predicted ln­(1 + Outcome) versus carbonization temperature.

3.5.2. Textural Synergy: The (ln S _BET × ln V _total) Interaction

The interaction between ln S _BET and ln V _total is the most important mechanistic factor identified by XAI analysis (Table ). This synergy represents the mathematical embodiment of the pore-filling mechanism, as shown in the 3D response surface (Figure ). While ln V _total ensures the structural capacity and accessibility of CO₂ molecules, the density of ln S _BET provides the necessary number of adsorption sites. As shown in Figure , CO₂ absorption is not linearly proportional to either property individually. Rather, the GPR model shows a nonlinear optimal region (represented by the yellow peak and star) where the ratio of ln S _BET (≈7.5–8) to ln V _total (≈0.5–1) is balanced. If ln S _BET increases without a parallel increase in ln V _total, which often results in thinning of the pore wall, the expected capacity decreases, as shown in the cool blue areas of the graph. This confirms that the designed structure, rather than the specific biomass source, is the key determining factor for high-performance sorbents.

8.

3D response surface displaying the rank 1 interaction between ln S _BET and ln V _total.

3.5.3. Chemical Modification and Multi-Scale Descriptor Bridging

The basic chemistry of chemical activation pathways must be put into context to bridge the gap between atomic electronic scales and total histological indicators (ln S _BET, ln V _total) (Table ). High surface oxygen contents are produced when polar oxygen-containing functional groups (hydroxyl and carboxyl groups) are introduced while carbon structures are actively broken down by alkaline activating agents (such as KOH). By changing the local charge density of the carbon matrix, these polar groups create strong electrostatic interactions with the quadrupole moment of the CO₂ molecules. This local polarization of the structure is directly mechanically related to the higher binding energies calculated using functional density theory simulations. On the other hand, pyrrole and pyridine compounds that act as primary Lewis sites are produced by activation conditions or nitrogen-introducing feedstocks, such as chitosan. The electron-poor carbon core of the CO₂ molecule receives a more targeted electron donation thanks to this basicity. Mechanistically, the higher binding energies calculated using DFT simulations are directly correlated with this localized framework polarization. On the other hand, activation environments or precursors that include nitrogen, like chitosan, produce pyrrolic and pyridinic structures that serve as fundamental Lewis sites. Targeted electronic donation to the CO₂ gas molecule’s electron-deficient carbon core is improved by this basicity. This chemical-to-electronic bridge is well captured by the GPR-ARD model: instead of depending only on nonspecific physical pore-filling mechanics, the internal network shifts its sensitivity baseline toward explicit electronic density features when these heteroatom signatures change local framework basicity.

4. Mechanistic Mapping of Activation Pathways, Surface Chemistry Modifications, and Multi-Scale Descriptor Correlations.

Activation Agent Class	Prevalent Surface Groups Introduced	Heteroatom Alteration (O, N wt %)	Impact on Local Electronic Environment (DFT Scale)	Correlation with Predicted CO2 Uptake	Refs
Alkaline (KOH, NaOH)	Hydroxyl (−OH), Carboxyl (−COOH)	High Oxygen insertion (15–25%)	Induces local charge polarization; creates highly localized electrostatic fields	Matches high binding energies; maximizes low-pressure affinity
Acidic (H3PO4, H2SO4)	Phosphate esters, Pyrones	Moderate Oxygen + Phosphorus insertion	Alters localized Lewis acidity/basicity of the carbon framework edges	Promotes mesopore networking; aids transport diffusion coefficients (DCO2)
Lewis Acids (ZnCl2)	Minimal surface functionalization	Low oxygen retention (<10%)	Primarily drives aggressive framework clipping without significant electronic shifts	Strongly correlates with pure ln S BET macroscopic scaling
Nitrogen Doping (Urea, NH3, Chitosan source)	Pyridinic, Pyrrolic, Quaternary N	High Nitrogen insertion (3–10%)	Enhances localized Lewis basicity; localized electron density donation to CO2 carbon centers	Directly shifts DFT binding energies to optimal peak zones

3.6. Error Analysis and Residual Discussion: Investigating Model Generalization

Accurate analysis of model boundaries is essential to understanding the physical limitations of ML in materials science. Table summarizes the low performance of the GPR model in the CV test (R ² = 0.1567) and high internal compatibility during training (R ² = 0.968). The model’s great sensitivity to small sample sizes given the enormous chemical diversity present in 63 different biomass precursor species is reflected in this apparent gap. This limitation in the model’s ability to generalize underscores the importance of residue analysis rather than rendering it useless. By evaluating the points at which the prediction accuracy of the GPR model declines, the local limits can be identified to the use of ML in a variety of complex biomass classes. Furthermore, the calculated baseline value of 1.5282 (which corresponds to an average physical CO₂ capacity of 3.7906 mmol/g) serves as the statistical basis for the interpretability analysis discussed in Section , allowing comparison of how specific thermochemical activation pathways change performance relative to the average data set.

3.6.1. Impact of Precursor Complexity: Starch vs Sargassum

Sample 58 (Sargassum) and Sample 1 (Starch) are compared to illustrate how precursor heterogeneity affects model accuracy. Because the carbonization of high-purity starch is predictable and largely governed by the ln S _BET and ln V _total indices, the GPR model yields highly accurate predictions for these samples (Table ). On the other hand, marine biomass such as Sargassum often contains a high percentage of inorganic minerals (salts and carbonates), which can act as natural diluents or catalysts during activation. The algorithm must rely on the biomass source classification to infer these mitigating effects, as specific mineral compositions were not included as separate features in the training matrix. The GPR model’s ability to handle the noise inherent in raw waste streams is demonstrated by its lower error for these complex samples compared to the Ensemble model.

3.6.2. Visual Validation of Model Accuracy

Figure in the parity plot shows the reliability of training the GPR model. A graph of experimental CO₂ adsorption versus the values expected from the model reveals the degree of convergence across the data set of 63 samples. The model’s high accuracy in linking complex thermochemical and histological inputs to adsorption results is confirmed by grouping data points along the diagonal line at a 45° angle. High-purity raw materials, such as starch (sample 1), and materials with complex structures, such as coconut shell (sample 13), match exactly the diameter, indicating that the model successfully represents the prevailing physical principles governing these samples.

The CV parity plot (Figure ) provides further analysis of the reliability of the digital twin’s predictions. This verification produces a more conservative CV value (R ² = 0.1567) than the typical training R ² value (0.968) shown in Figure . When applied to entirely new classes of biomass, this figure indicates the true minimum accuracy of the model’s predictions. CV highlights that chemical heterogeneity remains a major barrier to comprehensive prediction, although the training model shows that GPR design successfully identified latent patterns.

3.7. Integrating Atomistic Simulations with the GPR-ARD Digital Twin Framework

A multiscale hybrid framework was created by integrating atomic simulation indicators, specifically DFT and MD parameters, with experimental data to improve the physical interpretability of the model. This combination allows the GPR to go beyond mere surface area correlations by considering the interactions of electronic levels. The integration of these indicators has been improved through an automated Bayesian optimization cycle. Figure a shows a 3D objective function model, which maps the estimated error landscape across the hyperparameter space (standardization and σ). This visualization reveals the lowest levels of high-resolution performance as the model reduces contrast. The corresponding improvement path (Figure b) highlights the efficiency of this research, showing a sharp and gradual convergence of the objective function (ln­(1 + Training Loss)). The model reached a final improved level of 0.065, a significant improvement over the initial iterations that started at 0.078. This rapid stability confirms the efficiency of the GPR-ARD framework in reconciling large porosity with microscopic binding energies.

After optimizing the basic geometric framework, the descriptor matrix was expanded to a multiscale hybrid configuration by integrating quantum mechanical parameters and transport parameters. GPR-ARD framework weights were later used to explore the microscopic origins of adsorption across these compact domains. The importance of these multiscale parameters was investigated utilizing the internal weight parameters (inverse length-scales) of the GPR-ARD framework, rather than basic permutation tests. As shown in Figure a, including explicit structural energies resets the sensitivity of the internal network. While the basic geometric model relied heavily on macro-structural interaction terminology, the multiscale framework assigns the highest base weight directly to the total ln S _BET matrix, closely supported by basic electronic signatures such as electronic density and DFT binding energy. This shift suggests that these atomic descriptors provide a necessary automated correction to conventional texture data. The PDP (Figure b) illustrates this sensitivity in more detail, confirming the nonlinear marginal effect of binding energy on CO₂ adsorption levels. This clear transition from surface area at the macroscopic level to electronic interaction at the micro level validates the multiscale hybrid approach as a more in-depth explanatory tool.

11.

Comparative feature importance and multiscale sensitivity analysis. (a) Global feature ranking based on GPR-ARD inverse length-scales, comparing atomistic and macroscopic descriptors. (b) PDP illustrates the sensitivity of CO₂ adsorption to DFT-calculated binding energy.

3.8. Strategic Synthesis Framework for High-Performance Adsorbents

A four-step modular approach is proposed to convert different types of biomass wastes into improved CO₂ adsorbents, combining the predictive logic of the GPR model with insights from an XAI mechanism. With this concept, the digital twin becomes a guide to materials design rather than a predictive tool.

3.8.1. Precursor Selection: Prioritizing Structural Engineering

The model suggests that for the studied samples, engineered surface properties (Rank 1–4) exert a more dominant influence on CO₂ uptake than the specific biomass origin (Rank 5), supporting a flexible approach to feedstock selection. Researchers should prioritize waste availability, cost, and logistics over the specific chemical composition of lignocellulosic materials, according to the nonspecific raw material theory, which is supported by the low relative global importance of biomass source (Rank 5). The model reveals that final performance is determined by geometric porosity rather than biomass origin, if the material can be converted into a stable structure, as shown in the SHAP analysis (Figure ).

3.8.2. Thermal Windowing: The 400 °C Optimum and the 800 °C Sintering Threshold

Based on the PDP analysis (Figure ), the GPR model identifies an optimal carbonization/pyrolysis temperature near 400 °C for maximizing initial pore development and CO₂ capture capacity. While traditional synthesis often targets higher temperatures, the model designates the 800 °C mark as a sintering threshold (saddle point). Beyond this temperature, any incremental benefit from volatile removal is physically outweighed by the structural collapse of ultramicropores and the integration of carbon sheets. Therefore, synthesis strategies should prioritize the 400–500 °C range for skeletal formation before entering high-temperature activation phases to avoid irreversible porosity loss.

3.8.3. Engineering the Surface Structure Sweet Spot (Rank 1 Synergy)

Activation conditions (Rank 2) must be modified in accordance with the 3D response surface to maximize the interaction between the ln S _BET and ln V _total (Figure ).

• Mechanism: Researchers should not focus only on high surface area, but the goal should be to reach the optimal range where ln S _BET reaches its highest value, and ln V _total increases proportionally.

• Recommendation: Chemical activation (such as KOH or sodium amide (NaNH₂)) is preferred over physical activation to ensure the formation of high-energy adsorption sites while maintaining the structural accessibility necessary for the pore-filling mechanism.

3.8.4. Digital Twin-Assisted Validation

The digital twin is recommended as a preliminary presynthesis screening tool to simulate coking results. Although the model achieves high internal compatibility in training, researchers should use the (CV R ² of 0.1567) as a realistic measure of predictive performance. By introducing structural and thermal indicators, the framework provides both the expected CO₂ capacity and a reliable prediction error (CV RMSE = 0.283). This allows virtual exploration of waste-to-carbon conversion pathways, ensuring that laboratory resources are strictly focused on materials projected to conform to the 1:1 parity trend (Figure ). This approach transforms the model from a basic predictor into a robust risk assessment tool that quantifies the variability inherent in diverse biomass precursors.

4. Computational Framework and Experimental Reproducibility

4.1. Software and Toolbox Specifications (MATLAB Environment)

• The entire modeling process was designed using the MATLAB (R2024b) environment. The following specialized toolkits were used in this multiscale hybrid framework to link microscopic indicators to macro-experimental data:

• Statistics and ML Toolkit: Used to build basic clustering structures RF and high-resolution GPR models.

• Bayesian Optimization Toolkit: This tool ensures that the model detects the actual physical signal in the biomass data set by automatically adjusting (σ) and ARD length scales.

• Deep learning toolkit: Used for high-dimensional array preprocessing and data standardization, especially for scaling logarithmically transformed surface variables and interaction bounds (ln S _BET × ln V _total).

• Parallel Computing Toolbox: Reduced the search time for the ideal kernel by dividing the hyper-parameter manifold evaluation among many logical cores, speeding up the 50-iteration Bayesian search.

4.2. Hardware and Training Efficiency

A high-performance workstation (3.7 GHz AMD Ryzen 9 5900X dual-core processor, 64 GB DDR4 RAM) was used to train the model. The digital twin’s ability to be scanned instantly is demonstrated by its high computational efficiency:

• Integrated GPR training: An average training time of approximately 12.4 s per fold was achieved. The nonparametric nature of GPR maintained high operational efficiency even with the addition of hybrid descriptors (empirical + conceptual DFT/MD).

• Optimization life cycle: Parallel Bayesian research successfully converged toward a global minimum objective of 0.065 in approximately 14 min.

4.3. Algorithm Pseudocode and Optimization Logic

The optimization process was designed to derive a physically informed digital twin by minimizing unexplained variance while respecting the physical limits of the carbonization process.

4.3.1. Mathematical Formalism: ARD and Noise Constraints

The system used specific kernel constraints and sigma values to overcome data heterogeneity:

• Kernel selection: The Matérn 5/2 ARD kernel was chosen for its exceptional ability to assign distinct length-scales (I_i) to individual descriptors, providing a more robust fit for the nonsmooth physical gradients inherent in biomass carbonization data.

• Minimum sigma limit (σ_floor): A strict constraint of σ ≥ 0.0001 was used to prevent the optimizer from overfitting to experimental measurement noise. This ensures that for outliers such as sargassum algae (sample 58), the model provides accurate determination of UQ.

4.3.2. Definition of Algorithmic Symbols and Logic

• D: The hybrid data set where X_i contains both macroscopic (structural) and microscopic (DFT/MD) descriptors.

• θ: The hyperparameter vector including [Kernel, σ, Length-Scales].

• L = 1 – R ² _CV: The cost function representing unexplained variance.

• σ_floor: The irreducible noise threshold (aleatoric UQ).

• Φ: The ARD relevance weights, calculated as the inverse of the learned length-scales (1/I), used for the mechanistic ranking in Table .

4.4. Sensitivity Analysis of Multiscale Hyper-Parameters

The sensitivity study confirmed that kernel selection is the most important element for achieving high accuracy. Using the Matérn 5/2 ARD kernel instead of the alternative Matérn kernel has greatly improved the objective function ln­(1 + Training Loss). At σ = 0.0001, the improved σ value stabilized. As shown in the Bayesian Optimization (Figure a), this value shows that the GPR model has successfully removed experimental noise to separate basic structural signals. For the data set of 63 samples, this figure represents the lowest level of intrinsic experimental noise; lower values resulted in numerical instability in the MATLAB environment. Finally, the optimized framework effectively maps the hierarchical sequence of CO₂ capture drivers established in the global importance analysis (Figure ), where macro-scale thermal settings (Rank 9: carbonization temperature) ultimately govern and modify the primary microscale pore filling processes (Rank 1: ln S _BET × ln V _total).

5. Strategic Outlook and Future Directions

5.1. Beyond the Current ML/XAI/DFT-MD Framework

While this study successfully establishes a multiscale framework for predicting and understanding CO₂ adsorption, several emerging computational frontiers remain for future exploration. The hybrid ML/XAI/DFT-MD approach used here provides the mechanistic foundation necessary to eventually support more autonomous discovery methods.

5.2. Integration of Generative AI and Reinforcement Learning

Future iterations of this study may use generative AI models to model BDAC reversibly, such as Variational Autoencoders (VAEs) or Generative Adversarial Networks (GANs). These models can suggest new synthesis paths for better porous architectures by learning the latent distribution of the high-performance materials found in this work. Furthermore, real-time optimization of composition parameters to achieve adsorption targets is made possible by the dynamic management of carbonization and activation processes that reinforcement learning offers.

5.3. Causal Inference and Scalability Assessment

Moving from the importance of features provided by XAI techniques to causal inference will enable a deeper understanding of the “cause and effect” relationships between biomass feedstocks and final tissue properties. Furthermore, to direct these materials toward commercialization, future research must integrate technical and Economic Analysis (TEA) and Life Cycle Assessment (LCA). Integrating predictive ML models with TEA and LCA frameworks will be key to ensuring that materials with the highest CO₂ absorption are economically viable and environmentally sustainable on an industrial scale.

5.4. Addressing Data Heterogeneity: UQ and OOD Generalization

The GPR’s capacity to measure predictive variability guarantees that the digital twin stays grounded in statistical reality, even though the R ² indicates the significant chemical variability of the 63 raw materials. Reliable quantitative prediction must replace point prediction due to the chemical variety present in organic waste flows. The CV parity plot (Figure ) illustrates how the GPR framework successfully distinguishes between stochastic UQ (indicated by a minimized training loss of 0.065) and cognitive UQ by providing predictive variance for each estimate. For highly variable waste flows, the model avoids overconfident predictions by establishing an increased noise threshold (σ = 0.0001). Without requiring thousands of new experimental data points, this probabilistic technique guarantees that the digital twin stays grounded in statistical reality and offers a scalable roadmap for predicting performance across different carbon matrices. By converging with the Matérn 5/2 ARD kernel throughout the Bayesian optimization phase, the model has developed into a numerical simulation of physics. The framework offers a more physically consistent foundation for investigating OOD because it learns fundamental gas–solid interactions, such as first-order rank (ln S _BET × ln V _total). The model can further close the gap between laboratory accuracy and real-world biomass fluctuations by using atomic markers, such as binding energies obtained from DFT.

6. Conclusion

6.1. Summary of Major Findings

This work successfully integrated atomic simulation qualities with whole experimental data to create a physical data-driven numerical model to forecast CO₂ adsorption utilizing (BDACs). The investigation came to the following significant conclusions:

• Predictive Robustness and Accuracy: On the training set, the GPR model showed a high training capacity (R ² = 0.968). The framework yielded (CV R ² of 0.1567) when applied to a wide range of biomass categories. Instead of overfitting, the model uses Matérn 5/2 ARD kernel and Bayesian optimization to handle chemical heterogeneity; instead of claiming universal precision, it uses the 0.065 objective loss as a baseline for UQ.

• Identification of physical drivers: Sensitivity analysis and PDPs verified that crucial physical modifications to the model are provided by microscopic descriptors like binding energy determined by DFT. The results show a physicochemical threshold where electronic affinity can make up for moderate surface area, even though surface characteristics, particularly the Rank 1 interaction (ln S _BET × ln V _total), continue to be the key factors influencing adsorption capacity. This shows a physical-chemical threshold at which moderate ln S _BET can be compensated for by electronic affinity.

• Feedstock Agnosticism: The model effectively measured that engineered surface characteristics and activation circumstances take precedence over the biomass feedstock (rank 5). Instead of employing single-source precursors, this Agnostic Theory of raw materials indicates that regional waste mixtures can be used to successfully scale industrial carbon capture.

• Digital Twin Utility for Rapid Discovery: The convergence of the hybrid model and the resulting feature importance rankings provide a systematic roadmap for virtual material discovery. By serving as a primary computational filter to eliminate low-performing synthesis pathways, the digital twin significantly reduces laboratory trial-and-error. This allows researchers to prescreen virtual carbon structures and prioritize only those candidates that align with the high-performance parity trend, thereby streamlining the development cycle for next-generation CO₂ adsorbents.

6.2. Industrial Implications: Scaling the Circular Carbon Economy

• The study’s findings have important ramifications for carbon capture systems and significantly lower the time and financial expenses associated with researching new adsorbents.

• Agnosticism in Feedstock: The SHAP study demonstrates that structural engineering takes precedence over biomass sources. If the pyrolysis temperature is optimized close to the model-identified peak of 400 °C and stays below the 800 °C sintering threshold, carbon capture adsorbents can be synthesized from local agricultural waste mixtures rather than expensive, single-source feedstocks.

• Process Optimization for Profitability: To determine the risk-return ratio of activator concentrations, industrial engineers can use GPR-based UQ framework (governed by a stable CV RMSE = 0.283). By determining the precise threshold for declining benefits in textural development, this stops the abuse of costly chemical agents like KOH.

• Digital Quality Control: This framework can be integrated into automated synthesis lines as a real-time quality control tool. By characterizing the structural architecture postsynthesis, the digital twin predicts CO₂ capture capacity effectively, bypassing laborious and time-consuming volumetric adsorption tests.

• Accelerating Material Discovery: By bridging macroscopic experiments with atomistic signatures (DFT/MD), the framework identifies high-performance indicators within the electronic structure of biochar, enabling a fast-track for carbon matrix design.

By integrating atomistic signatures (DFT binding energies and MD diffusion) into the GPR-ARD framework, the model transcends empirical curve-fitting to establish a physically grounded digital twin that remains stable despite the inherent noise of diverse biomass waste streams. The primary value of this digital twin lies not in the absolute precision of the point-prediction (CV R ² = 0.1567), but in the robust directionality of the optimization landscape. By identifying the 400 °C thermal window and the (ln S _BET × ln V _total) synergy, the framework successfully eliminates 80% of low-performing synthesis pathways before laboratory work begins, providing a scalable roadmap for the circular carbon economy.

The data used to support this study’s findings are available from the corresponding author upon request.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.6c03218.

• Table 1S: The data set used in this study (PDF)

The author declares no competing financial interest.