Bridging Physics and Data Hybrid Modelling of NOx and Soot Emissions in Alternative-Fuel Diesel Engine

Abstract

Keywords: Ammonia; Biodiesel; Machine learning; Emission prediction; Physically informed model

1. Introduction

As long as humanity exists, the demand for energy will continue. A significant portion of this demand is still met today through internal combustion engines and turbine-based energy conversion systems. Although these systems operate on different principles, they share a common challenge in

achieving environmental sustainability, which is the reduction of harmful emissions. Emission species such as carbon dioxide (CO2 ), carbon monoxide (CO), nitrogen oxides (NOx), unburned hydrocarbons (HC), particulate matter (PM), sulfur oxides (SOx), aldehydes, and soot produced during energy conversion pose serious risks to both the environment and human health. In the maritime sector, the

Received 18 November 2025; revised 31 December 2025; accepted 5 January 2026. Published online 19 January 2026 E-mail address: f.okumus@mersin.edu.tr (F. OKUMUŞ). https://doi.org/10.29187/2792-0771.1044 2792-0771/© 2026 Published by Yıldız Technical University Press, İstanbul, Türkiye. This is an open access article under the CC BY-NC 4.0 Licence (https://creativecommons.org/licenses/by-nc/4.0/).

International Maritime Organization (IMO) has implemented increasingly stringent regulations to limit harmful emissions from marine diesel engines (Göksel, 2022). Therefore, research has increasingly focused on developing and applying alternative fuels. Alternative fuels offer advantages over fossil fuels because they can be produced from renewable resources and have the potential to reduce the carbon footprint. However, they may also adversely affect combustion characteristics, engine performance, and certain types of emissions. Thus, although alternative fuels present clear environmental advantages, they simultaneously introduce challenges and unfavourable effects in combustion behaviour that warrant thorough investigation. To investigate these interactions, the literature primarily employs experimental or numerical methods such as Computational Fluid Dynamics (CFD). Experimental studies can provide reliable insights into engine behaviour through direct measurements. Yet, their scope is often limited due to high costs, time requirements, equipment needs, measurement uncertainties, and repeatability issues. Moreover, examining every possible fuel combination experimentally is neither economically nor environmentally sustainable. In this regard, CFD-based combustion simulations have become powerful tools, as they can analyze in-cylinder flow, turbulence, heat transfer, and chemical reactions in three dimensions. Detailed reaction mechanisms and optimized combustion models enable high-fidelity prediction of emissions such as CO, CO2 , unburned hydrocarbons (HC), methane (CH4 ), formaldehyde (HCHO), and nitrous oxide (N2 O). Since these emissions are closely related to combustion efficiency and the air–fuel ratio, modern CFD solvers can represent these effects effectively using chemical kinetic models. This complexity makes modelling difficult (Z. Wang & Yang, 2024). Furthermore, the intricate nature of chemical mechanisms imposes additional limitations. For instance, accurate NOx prediction typically requires detailed reaction paths such as the Zeldovich mechanism (Barış, 2024), while soot modelling involves processes like nucleation, coagulation, and oxidation occurring at different spatial and temporal scales (Curinao et al., 2024). Researchers employ engine simulators (Karatuğ, 2025) and CFD-based numerical studies (Kanberoğlu et al., 2025) to analyze combustion processes and develop strategies for minimizing harmful emissions from diesel engines. CFD simulations also depend on numerous user-defined parameters and empirical sub-models, which demand careful calibration. NOx and soot predictions are highly sensitive to these parameters and must be re-tuned for each new engine

geometry or fuel type (Shaparia et al., 2024). Similarly, mesh resolution and time-step selection critically influence simulation accuracy. High-resolution meshes and small time steps are required to resolve turbulence and temperature gradients accurately, but they significantly increase computational cost (Sofos et al., 2025). The complexity of modelling increases further with the introduction of alternative fuels. Low-carbon or carbon-free fuels such as biodiesel (Testa et al., 2024) and ammonia (NH3 ) (Okumuş et al., 2024) are promising for diesel engines from an environmental perspective. Yet, their distinct physical and chemical properties complicate accurate NOx and soot predictions. In the case of biodiesel, the primary modelling challenge arises from compositional variability. The fatty acid methyl ester (FAME) composition of biodiesel varies depending on the feedstock, such as soybean, rapeseed, palm, or waste oil. This variability affects its chemical properties and makes it challenging to develop universally applicable reaction mechanisms and parameter settings in CFD models (Zettervall & Nilsson, 2024). Moreover, biodiesel’s high oxygen content increases combustion temperature and promotes NOx formation while simultaneously reducing soot due to its oxygenated structure. These opposite effects require careful balancing to maintain model accuracy (Yang et al., 2025). Biodiesel’s high viscosity also affects spray behavior, atomization quality, and air–fuel mixing, leading to less homogeneous combustion. Since these physical differences directly influence NOx and soot formation, accurate predictions are only possible with detailed spray and atomization sub-models (Radha Srikakolapu et al., 2025). Similarly, ammonia presents unique challenges for CFD modelling. It has a long ignition delay and a low flame speed, leading to low-stability combustion zones and prolonged combustion durations, which in turn promote high NOx formation (Mashruk et al., 2024). In addition to NO and NO2 , unburned NH3 and N2 O also become significant emission components. Accurately predicting these species requires advanced nitrogen chemistry models beyond the classical Zeldovich approach (Mashruk et al., 2024). Furthermore, since ammonia alone often fails to provide stable combustion, it is typically blended with fuels like hydrogen or biodiesel. Modelling the combined effects of different flame speeds, turbulence intensities, and energy release rates within a single framework further increases the complexity (Sun et al., 2025; Wu et al., 2023). Consequently, traditional CFD-based methods remain limited in both computational efficiency and

model validation, particularly for multi-fuel diesel engines. At this point, data-driven modelling techniques, especially those based on machine learning (ML), have gained growing attention. ML algorithms can achieve high-accuracy predictions by learning statistical relationships directly from observational data, without explicitly modelling every physical process. In ML-based emission prediction models, the selection of input variables is critical for both accuracy and generalization. Literature studies employ a wide range of measured and calculated parameters representing actual engine operating conditions. For instance, a deep learning-based NOx prediction study identified engine speed, torque, EGR valve position, exhaust flow, air mass flow, and oil temperature as the most influential inputs (Qiu et al., 2024). In another study using artificial neural networks and OBD data, vehicle speed, engine speed, torque, coolant temperature, air–fuel ratio, and intake airflow were used to predict CO2 , CO, and NOx emissions with high accuracy (Seo & Park, 2023). In a model employing dimensionality reduction, 37 parameters were initially considered, and injection pressure, fuel flow rate, exhaust temperature, in-cylinder pressure, and turbo pressure were found to be dominant (Mohammad et al., 2023). For marine engines, parameter sets such as engine speed, load, fuel flow, air mass flow, and injection pressure are widely used due to their relevance to large-scale systems (M. Wang et al., 2010). Studies addressing both diesel and gasoline engines customize input variables such as air flow, boost pressure, fuel flow, load, cycle number, and ignition timing according to engine type (Tütüncü & Allahverdi, 2009). Collectively, these findings highlight the importance of selecting inputs that are both physically meaningful and information-rich with respect to the target emission type and engine architecture. In this study, the selected input parameters are directly linked to NOx and soot formation mechanisms not only statistically but also through their physical and thermodynamic foundations. The parameters include IMEP (Indicated Mean Effective Pressure), MPRR (Maximum Pressure Rise Rate), Pmax (Maximum Cylinder Pressure), Pmax_CA (Crank Angle at Pmax), CA10–CA90 intervals, ignition delay, and combustion duration. Each of these indicators represents fundamental dynamics of the combustion process. IMEP reflects the engine’s overall energy efficiency, while MPRR and Pmax are closely related to combustion intensity and high-temperature regions, which are crucial for thermal NOx formation. The CA10– CA90 interval and combustion duration influence the

heat release rate and mixture homogeneity, affecting soot formation tendencies. Ignition delay determines the premixed fraction and early chemical kinetics, influencing both NOx and soot in opposite directions. Crank angle at Pmax indicates combustion phasing and forms a strong link between combustion efficiency and emission characteristics. Despite the growing number of studies employing machine learning techniques for emission prediction in internal combustion engines, most existing models rely predominantly on easily accessible operational parameters or fuel type information, treating the combustion process as a black box. Such approaches often achieve acceptable accuracy within limited operating ranges but lack physical interpretability and robustness, particularly under multi-fuel and alternative fuel conditions. In contrast, the present study explicitly integrates combustion-derived physical indicators obtained from in-cylinder pressure measurements into the machine learning framework. By incorporating parameters such as IMEP, maximum pressure rise rate, combustion phasing, ignition delay, and CA10–CA90 duration, the proposed model embeds thermodynamic and chemical combustion characteristics directly into the datadriven structure. This hybrid, physically informed approach differs fundamentally from conventional fuel-based or purely statistical models by linking emission formation to underlying combustion dynamics. The main contribution of this study is the demonstration that physically informed feature integration significantly enhances prediction accuracy, reduces systematic bias, and improves generalization for both NOx and soot emissions, particularly for biodiesel- and ammonia-based fuel strategies.

3. Results and discussions

In this study, two different modelling approaches were evaluated for the prediction of NOx and soot emissions. The first approach, the Basic model, is a fundamental machine learning framework that utilizes only fuel types (diesel, biodiesel, and ammonia) as input variables and does not incorporate any physical parameters related to the combustion process. This model aims to statistically capture the general tendency of emission formation based on fuel composition and represents the simplest reference level for comparison, as it contains no information about the underlying physical processes. In contrast, the Physically Informed model includes not only fuel types but also combustion related parameters derived from experimental in-cylinder pressure data, such as IMEP, MPRR, Pmax, Pmax_CA, CA10–CA90, ignition delay, and combustion duration. By integrating these variables, the model reflects the chemical, thermodynamic, and temporal dynamics governing emission formation, thereby providing a physically coherent prediction framework. The development of both models involved data processing, derivation of

combustion indicators, RFE-based feature selection, evaluation of model complexity using BIC, implementation of linear regression, Random Forest, and Gradient Boosting algorithms, hyperparameter optimization, and final assessment using R2 and RMSE performance metrics. In this context, the primary objective of the Results and Discussions section is not merely to compare the overall predictive accuracy of the models, but rather to highlight the performance distinction between the Basic and Physically Informed models and thereby assess the effect of incorporating physical knowledge into the prediction framework. When evaluating the results in Fig. 7, it is observed that the Basic model exhibits significant deviations from the reference line in both NOx and soot predictions. Using only fuel type as an input variable, this model systematically underestimated predictions, particularly at high NOx and medium-to-high soot levels. The wide dispersion of data points indicates that the model fails to represent the physical dynamics of the combustion process. In contrast, the Physically Informed model, thanks to the use of parameters that directly reflect combustion physics,

Fig. 8. Comparison of basic and physically informed models for NOx and soot prediction using linear regression.

such as IMEP, MPRR, Pmax, Pmax_CA, CA10–CA90, and ignition delay, provided a distribution much closer to the reference line in both NOx and soot predictions, with a noticeable reduction in deviations. In particular, the improvement in NOx predictions at high values and the tight clustering at low levels in soot predictions demonstrate that incorporating physical information into the model significantly increases prediction success. These findings are consistent with the fact that emission formation mechanisms are highly sensitive to physical processes such as excess combustion, pressure rise rate, combustion time, and mixture formation, independent of fuel type, confirming that the Physically Informed model offers a much more reliable and physically grounded prediction structure compared to the Basic model. The Random Forest results presented in Fig. 8 show that the performance difference between the Basic and Physically Informed models is consistent with the trends observed in the Linear Regression model, but is more pronounced. In the Basic model, both NOx and soot predictions show significant deviations from the reference line and exhibit a systematic underestimation tendency, particularly at high NOx

levels. This situation, as in the Linear Regression results, demonstrates that a model based solely on fuel type is insufficient to represent the complex physical dynamics of the combustion process. In contrast, the Physically Informed model shows data points clustered much closer to the reference line, with a marked improvement in prediction accuracy for both training and test data. This improvement parallels the performance increase seen in the Linear Regression model, but achieves greater success due to the Random Forest’s ability to capture non-linear relationships. Particularly in soot predictions, the significant reduction in the high dispersion observed in the Basic model demonstrates that the effect of including physical combustion parameters in the model is more pronounced in the Random Forest structure. Overall, the results in Fig. 3 clearly demonstrate that the Physically Informed model offers a much superior prediction performance compared to the Basic model in both linear and non-linear approaches. The Gradient Boosting results presented in Fig. 9 demonstrate that the performance difference between the Basic and Physically Informed models is most pronounced among the three methods used in this study.

Fig. 9. Comparison of basic and physically informed models for NOx and soot prediction using GBM.

Although the Basic model shows better fit in both NOx and soot predictions compared to Linear Regression and Random Forest results, it is noteworthy that the data points still exhibit significant deviations from the reference line and a pronounced tendency to underestimate at high soot levels. This situation once again confirms that models that do not incorporate combustion physics cannot fully represent complex emission processes. In contrast, the Physically Informed model, combined with the Gradient Boosting algorithm, provided the highest accuracy among all models; it was observed that the data points showed an almost ideal alignment on the reference line in both the training and test sets. This result demonstrates that the data structure enriched with physical parameters, when combined with the sequential learning mechanism of Gradient Boosting, significantly improves emission prediction performance. In particular, the attainment of a nearerror-free distribution in NOx predictions and the much lower deviations in soot predictions compared to previous models demonstrate that the strongest effect of incorporating physical information into the model emerges under the GBM structure. Overall,

Fig. 4 clearly shows that the Physically Informed model, in conjunction with the Gradient Boosting algorithm, delivered the most successful and reliable prediction performance in this study. In the study, residuals are expressed as percentage deviations rather than absolute differences and are presented in violin plot format in the Figure. The percentage residual shows how much and in which direction the model estimate deviates from the actual measurement for each data point. This approach aimed to evaluate the relative magnitude of error in emission components with different size ranges, such as NOx and soot, on a comparable scale. The violin plots in the figures now show the density structure of the value distribution, with black boxes (25th–75th percentile range), black line extensions (1.5×IQR range) and a white dot (median) indicating the position and spread of the distribution. Fig. 10 shows the percentage residual distributions obtained for NOx and soot predictions using the Basic and Physically Informed models. In the Basic model, the residual distributions for both NOx and soot are spread over a wider range, with median values below zero; this indicates that the model has a systematic

Fig. 10. Percentage residual distributions for NOx and soot predictions using linear regression.

Fig. 11. Percentage residual distributions for NOx and soot predictions using random forest.

tendency to underestimate. In contrast, the Physically Informed model shows a significantly narrower distribution, fewer extreme values, and a median approaching zero. This improvement demonstrates that incorporating physical combustion parameters into the model not only reduces error but also significantly eliminates the model’s prediction bias.

Fig. 11 shows the percentage residual distributions for NOx and soot estimates obtained using the Random Forest model. In the basic model, it is noteworthy that the residual distributions for both NOx and soot are spread over a fairly wide range, with extreme deviations of up to ±150% observed, particularly in the soot component. This

Fig. 12. Percentage residual distributions for NOx and soot predictions using GBM.

situation demonstrates that approaches lacking physical parameters are limited in representing the complex character of emission formation, despite the non-linear learning capacity of Random Forest. In contrast, the Physically Informed model shows a significantly narrowed distribution, with extreme values substantially reduced and median values approaching zero. This improvement demonstrates that adding combustion physics variables such as IMEP, MPRR, Pmax, and CA10–CA90 to the model creates a strong interaction under the Random Forest structure and significantly reduces prediction errors in terms of both magnitude and direction. In particular, the residual distribution becoming more compact for NOx and the convergence of the median on the soot side becoming more pronounced clearly demonstrate that the Physically Informed model, combined with the Random Forest algorithm, has significantly improved emission prediction performance. Fig. 12 shows the percentage residual distributions for NOx and soot estimates obtained using the Gradient Boosting model. In the basic model, it can be seen that the residual distributions for both emission components are still spread over a relatively wide range and that there are significant deviations, particularly in the negative direction, in the soot predictions. However, the fact that the distribution is more compact compared to the Linear Regression and Random Forest models confirms that the sequential learning structure of Gradient Boosting naturally reduces the

error. In the Physically Informed model, the residual distributions reach their narrowest form, extreme values almost completely disappear, and median values approach zero. This demonstrates that physical combustion parameters, when combined with Gradient Boosting’s structured learning process, maximise emission prediction accuracy. Particularly in NOx predictions, the residual distribution concentrating within a very low range and the elimination of systematic errors on the soot side clearly demonstrate that the Physically Informed model exhibits the most stable and lowest bias prediction performance among the three methods used in this study under Gradient Boosting. Table 2 comprehensively presents the NOx and soot prediction performance of the Basic and Physically Informed models under three different regression algorithms—Linear Regression, Random Forest, and Gradient Boosting Machine. When the results are evaluated overall, it is seen that adding physical combustion parameters to the model provides a consistent performance increase in all methods. In the Linear Regression results, it is noteworthy that the R2 values for the Basic model remained at 0.37 for both the training and test sets in NOx prediction, whereas these values increased to 0.84 for training and 0.81 for testing in the Physically Informed model. The same trend is observed in the RMSE and MAE values, with the RMSE in the Basic model ranging from 408 to 322 ppm, while in the Physically

Table 2. Performance metrics (R2 , RMSE, MAE) of basic and physically informed models for NOx and soot prediction across all regression algorithms. Algorithm

Train Test Train Test Train Test Train Test Train Test Train Test Train Test Train Test Train Test Train Test Train Test Train Test

Informed model it is reduced by approximately half (204–243 ppm). and the MAE decreasing from 305–255 ppm to 146–181 ppm, indicating that physical inputs provide a significant improvement for linear regression. A similar trend is observed in soot predictions, where the test R2 value of the Basic model is only 0.46, while in the Physically Informed model this value increases to 0.58, RMSE decreases from 0.47 to 0.25, and MAE decreases from 0.23 to 0.12. Random Forest results offer significantly higher accuracy compared to Linear Regression, and performance has improved further with the inclusion of physical parameters. For NOx, the R2 values of the Basic model ranged from 0.74 to 0.78, while the Physically Informed model brought these values to 0.84–0.82 levels. MAE values decreased from 142–157 ppm to 87–117 ppm, and RMSE decreased from 226–229 ppm to 190–220 ppm. For soot prediction, RF was one of the most successful methods, with the Basic model’s test R2 value at 0.92, while the Physically Informed model increased this value to 0.99. Furthermore, the decrease in the test RMSE for soot from 0.21 to 0.06 and the MAE from 0.17 to 0.03 demonstrates that the physical combustion parameters provided a very strong and clear improvement in particle formation estimation. The trends observed in Table 2 are consistent with findings reported in previous studies on physics-informed and combustion-feature-based ma-

chine learning models applied to emission prediction. Several studies have shown that incorporating physically meaningful combustion parameters, such as IMEP, pressure rise rate, and combustion phasing, significantly improves prediction accuracy for NOx and soot compared to models relying solely on fueltype or operating-condition inputs (Alessandro et al., 2025). Similar reductions in prediction error and improvements in model robustness have been reported in recent works focusing on hybrid data-driven– physics-based frameworks for internal combustion engines (Z. Chen et al., 2025). Therefore, the results presented in Table 1 are in good agreement with the existing literature and further confirm the effectiveness of incorporating combustion-derived features into emission prediction models. Despite the strong prediction performance achieved by the physically informed models, several limitations of the present study should be acknowledged. First, the dataset was obtained from a single-cylinder diesel engine operated at a fixed engine speed and limited load conditions. Therefore, the trained models may not directly generalize to engines with different geometries, combustion systems, or transient operating conditions without retraining or recalibration. Also, we acknowledge that the physically informed features used in this study rely on highresolution in-cylinder pressure measurements, which historically represented a limitation for practical

implementation, particularly in applications where continuous pressure monitoring was not available. In large marine main engines, however, in-cylinder pressure has long been obtained routinely through indicator valves for combustion analysis and performance assessment, albeit typically on a periodic rather than continuous basis. With the progressive adoption of modern electronically controlled marine engines and advanced condition monitoring systems, access to combustion-related parameters has been steadily improving. Consequently, key combustion indicators such as IMEP, pressure rise rate, combustion phasing, and combustion duration are no longer purely experimental quantities but are increasingly becoming practically accessible parameters in marine applications. While the absolute model coefficients remain engine-specific, the proposed modelling strategy is therefore transferable and can be progressively extended to different marine engine types, fuel combinations, and operating conditions, provided that appropriate training data are available. The improved prediction capability obtained by incorporating combustion-related parameters can be directly linked to well-established NOx and soot formation mechanisms in diesel and dual-fuel combustion. Nitrogen oxide formation in compression ignition engines is predominantly governed by the thermal (Zeldovich) mechanism, which exhibits an exponential dependence on local flame temperature and residence time at high temperatures (Marinović & Mitrović, 2025). Parameters such as IMEP, maximum pressure, maximum pressure rise rate, and ignition delay provide indirect but physically meaningful information about in-cylinder temperature levels, combustion intensity, and heat release phasing. Ignition delay and higher MPRR generally indicate more intense premixed combustion, leading to elevated peak temperatures and, consequently, increased NOx formation, as widely reported in the literature (Qin et al., 2026; Shen et al., 2025). Similarly, soot formation is strongly influenced by local equivalence ratio, mixing quality, and combustion duration (Koob et al., 2026). The CA10– CA90 combustion interval and total combustion duration reflect the temporal evolution of fuel–air mixing and oxidation processes within the cylinder. Extended combustion durations and delayed heat release phases tend to promote fuel-rich regions and incomplete oxidation, favouring soot formation, whereas improved mixing and more homogeneous combustion reduce soot levels. In addition, variations in heat release characteristics observed under different fuel strategies, particularly in dual-fuel and high-ammonia conditions, alter flame structure and oxidation pathways, further affecting soot emissions (C. Chen & Liu, 2023). Therefore, the inclusion of

these combustion indicators allows the model to implicitly capture the underlying thermochemical processes governing NOx and soot formation, explaining the observed reduction in prediction error beyond purely statistical improvements.

4. Conclusions

In this study, a fuel type based fundamental model for estimating NOx and soot emissions in diesel engines was comparatively evaluated against a physicsbased model incorporating combustion characteristics derived from in-cylinder pressure data. The impact of parameters such as IMEP, maximum pressure rise rate, maximum pressure, Pmax-CA, CA10–CA90, ignition delay, and total combustion time, integrated into the physical model, on emission prediction performance has been quantitatively analysed. The results obtained show that the physics-based model provides a significant increase in accuracy compared to the basic model in all machine learning algorithms. In the linear regression model, the test R2 value of the basic NOx model was 0.37, while in the physics-based model, this value increased to 0.81; RMSE decreased from 322 ppm to 243 ppm, and MAE decreased from 255 ppm to 181 ppm. The contribution of physical information in the Random Forest algorithm has become more pronounced; while the test R2 value of the basic NOx model was 0.78, it reached 0.82 in the physics-based model. The NOx RMSE value decreased from 229 ppm to 220 ppm, and the MAE decreased from 157 ppm to 117 ppm. In temperature estimation, although the basic model had a test R2 value of 0.92, the physicsbased model increased this value to 0.99; the test RMSE decreased significantly from 0.21 to 0.06, and the MAE decreased from 0.17 to 0.03. The highest accuracy was achieved with the Gradient Boosting Machine (GBM) method. While the test R2 value for NOx was 0.88 in the basic GBM model, the physics-based model reached 0.99. The test RMSE decreased significantly from 187.6 ppm to 43.1 ppm, and the MAE decreased significantly from 130.8 ppm to 28.1 ppm. For the Is component, the test R2 value of the basic model was 0.94, while the physics-based model reached a value of 0.99; the RMSE decreased from 0.19 to 0.05, and the MAE decreased from 0.17 to 0.02. These numerical findings demonstrate that integrating cylinder pressure-based combustion indicators into the model provides high accuracy in predicting both NOx and soot emissions. The physics-based approach, particularly with the Gradient Boosting method reaching an R2 of 0.99, has provided the most reliable prediction framework for representing the emission behaviour of alternative fuel strategies.

Indicated Mean Effective Pressure (bar) Maximum Pressure Rise Rate (bar/°CA) Maximum in-cylinder pressure (bar) Crank angle corresponding to maximum in-cylinder pressure (°CA) Crank angle interval between 10% and 90% cumulative heat release, representing combustion duration (°CA) Cumulative Heat Release — total energy released as a function of crank angle Heat Release Rate Ignition Delay Bayesian Information Criterion Recursive Feature Elimination Random Forest Gradient Boosting Machine Out-of-Bag Root Mean Square Error Mean Absolute Error Coefficient of Determination Number of trees in Random Forest Number of boosting iterations in Gradient Boosting Machine Maximum depth of individual trees in Gradient Boosting model Learning rate controlling contribution of each weak learner in GBM Minimum number of observations per terminal node (tree leaf) Ammonia — alternative fuel used in dual-fuel operation Diesel–biodiesel blend ratios by volume (%) Carbon monoxide, carbon dioxide, hydrocarbons, nitrogen oxides, sulfur oxides, particulate matter Fuel type based machine learning model without combustion parameters Data-driven model incorporating combustion-derived physical indicators Input configuration including physical combustion parameters (e.g., IMEP, MPRR, CA10–CA90) Baseline input set including only fuel type variables

CHR HRR ID BIC RFE RF GBM OOB RMSE MAE R2 nTree n.trees interaction.depth shrinkage n.minobsinnode NH3 B0, B20, B40, B100 CO, CO2 , HC, NOx, SOx, PM Basic Model Physically-Informed Model Enhanced Feature Set Standard Input Configuration

Nomenclature

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The author declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Author contribution

The entire study, “Bridging Physics and Data: Hybrid Modelling of NOx and Soot Emissions in Alternative-Fuel Diesel Engine” was conducted by Fatih OKUMUŞ.

Data availability

The datasets generated and analyzed during the current study are not publicly available due to their use in ongoing research but are available from the corresponding author on reasonable request.

Funding statement This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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