An Integrated Approach for Generating Reduced Order Models of the Effective Thermal Conductivity of Nuclear Fuels

Abstract

Accurate prediction of the effective thermal conductivity (ETC) of nuclear fuels is essential for optimizing fuel performance and ensuring reactor safety. However, the experimental determination of ETC is often limited by cost and complexity, while high-fidelity simulations are computationally intensive. This study presents a novel hybrid framework that integrates experimental data, validated mesoscale finite element simulations, and machine-learning (ML) models to efficiently and accurately estimate ETC for advanced uranium-based nuclear fuels. The framework was demonstrated on three fuel systems: UO₂-BeO composites, UO₂-Mo composites, and U-10Zr metallic alloys. Mesoscale simulations incorporating microstructural features and interfacial thermal resistance were validated against experimental data, producing synthetic datasets for training and testing ML algorithms. Among the three regression methods evaluated, namely Bayesian Ridge, Random Forest, and Multi-Polynomial Regression, the latter showed the highest accuracy, with prediction errors below 10% across all fuel types. The selected multi-polynomial model was subsequently used to predict ETC over extended temperature and composition ranges, offering high computational efficiency and analytical convenience. The results closely matched those from the validated simulations, confirming the robustness of the model. This integrated approach not only reduces reliance on costly experiments and long simulation times but also provides an analytical form suitable for embedding in engineering-scale fuel performance codes. The framework represents a scalable and generalizable tool for thermal property prediction in nuclear materials.

1. Introduction

Thermal conductivity plays a major role in nuclear fuel performance. Since thermal conductivity controls the operating temperature and temperature gradient of nuclear fuel, it influences not only the fuel performance but also the safety and efficiency of nuclear power plants. For instance, it has a strong impact on microstructural evolution processes in fuels such as the diffusion of lanthanides elements [1], gas bubbles migration [2], and constituent redistribution [3]. However, the prediction of the effective thermal conductivity for various nuclear fuels is a cumbersome task due to the synergistic effects of microstructure, composition, temperature, and irradiation. This is evident from several studies in the literature that focus on this important issue, utilizing experimental methods [4,5,6] or modeling and simulation techniques [7,8,9]. Each of these tools has its own challenges. For instance, the experimental data of many nuclear materials are limited due to the high cost and technical challenges of conducting these experiments. Furthermore, conducting physics-based simulations to predict effective thermal conductivity requires high computational power in addition to long running times.

Recent research has increasingly leveraged machine learning (ML) and deep learning (DL) to predict the effective thermal conductivity of nuclear fuels, a critical parameter for fuel performance and safety analysis. Traditional ML models, including linear regression, support vector machines, and random forests, have been successfully employed to establish robust relationships between operational parameters and thermal conductivity. For instance, these models effectively predict the thermal conductivity of uranium dioxide (UO₂) and mixed-oxide (MOX) fuels by using input features such as temperature, porosity, stoichiometry, and burnup, which are readily available from simulations or experimental data [10,11]. These regression-based approaches offer a computationally efficient alternative to complex physics-based models, providing rapid and accurate predictions that can be integrated into multiscale fuel performance codes.

Concurrently, the application of deep neural networks (DNNs) has enabled more nuanced predictions by capturing highly complex, nonlinear dependencies within the data. DNNs and specialized architectures like convolutional neural networks (CNNs) are being used to directly link microstructural features to thermal properties. By training on datasets of fuel microstructures, often generated through phase-field simulations or obtained from microscopic imaging, CNNs can learn to identify and quantify the impact of features like grain size, fission gas bubble distribution, and pore morphology on thermal conductivity without requiring manual feature extraction [12]. These models were also utilized for metallic fuels such as U-Mo [13] and U-10Zr [14]. This ability to learn directly from high-dimensional data allows for a more fundamental, microstructure-aware prediction of thermal properties, representing a significant step toward developing predictive tools that can accelerate the design and qualification of advanced, accident-tolerant fuels. Hence, machine-learning (ML) methods present a promising solution to overcome these obstacles.

Here, we present an integrated approach to predict the effective thermal conductivity of nuclear fuels that combines the results obtained via different methods, e.g., experiments, physics-based simulations, and ML algorithms. This hybrid approach is intended to benefit from the merits of each technique while avoiding their shortcomings. This could be successfully achieved via the following procedure. First, collect or obtain a few datasets on the fuel of interest. These sets need not be large or comprehensive. Second, perform simulations of the physics-based models of the effective thermal conductivity of this fuel. Third, validate the simulations using available data. Fourth, conduct more physics-based simulations to produce synthetic data for the extended training and/or testing of the ML algorithms since the experimentally validated simulations can now be considered as “digital twins” of the corresponding experiments. Lastly, select the best-performing ML algorithm or algorithms as the most efficient reduced order model for predicting the effective thermal conductivity of this specific fuel (or fuels).

The present work details the implementation of the procedure for three distinct types of nuclear fuels. We first list the available experimental data for these nuclear fuels that were used to validate the physics-based models. We then summarize the physics-based models that were first developed and then used to generate data for the testing stage. The optimum ML algorithm is selected at the end of the testing stage and then utilized as the model of choice for the production stage.

2. Materials and Methods

The integrated model incorporates three main components, e.g., experimental data for three common nuclear fuels, physics-based models implemented by validated high-fidelity finite element simulations, and various ML algorithms. The main principle here is to use the first component (the conducted experimental data for various types of nuclear fuel) to validate the second component (the developed physics-based models); then, integrate both of those components with the third component to facilitate the prediction of the effective thermal conductivity for the various nuclear fuels. Since the developed physics-based models are validated versus the experimental data, the training stage was chosen to be executed using the experimental data, and the testing stage with predictions of the developed physics-based models. A schematic illustration of this approach is presented in Figure 1. The details of each component of the integrated model are presented in the following subsections. Two of the physics-based models were developed in our previous work (UO2-BeO [9] and U-Zr [15]), and the third one (UO2-Mo) is developed through this work.

2.1. Experimental Data

In this work, we demonstrate the accuracy and efficiency of our hybrid approach by applying it to three distinct nuclear fuels, e.g., UO2-BeO, UO2- Mo composite fuels and U-Zr metallic fuel. First, one should collect the available experimental data to validate the physics-based models. While it is generally unnecessary to require huge datasets, they should contain data points to verify the effects of primary parameters/variables in the physics-based model. For the calculations of the effective thermal conductivity of nuclear fuels, those primary variables are temperature, volume fraction of phases, and/or porosity fractions [9,10,11,12,13,14,15]. We list the range of those variables for the three nuclear fuels selected for this study in

Table 1. The experimental data used to validate the physics-based models and in the training stage for the ML algorithms.

Fuel	Temperature Range (°C)	Increment (°C)	Compositions	Reference
UO2-BeO	25–300	25	5, 10, and 15 (BeO Vol%)	[9]
UO2-Mo	300–1200	100	2, 5, and 10 (Mo Vol%)	[8]
U-Zr	40–300	10	74, 78, 82, and 84 (TD *%)	[6,15]

* TD: theoretical density.

. Note that some of these datasets were parts of our earlier works with our collaborators [9,10,15].

2.2. Physics-Based Model Formulation

The physics-based model of choice here is a mesoscale model that directly accounts for microstructural features such as phase fractions, porosity, interface thermal resistance, and temperature on the effective conductivity [9,15,16,17,18,19,20]. These types of models are usually implemented using a microstructure-informed finite-element method. We briefly summarize here the main components of these models.

2.2.1. Thermal Model

The first part of the model is the thermal component, which solves the heat conduction equation in a heterogeneous medium representing the underlying microstructure. For simplicity, we employ two-dimensional (2D) simulations of the model, but the approach remains applicable without modification in three-dimensional (3D) simulations. Typically, constant temperatures T_r and T_l are applied on the right and left side (x direction), respectively. The other two boundaries (y direction) are taken as adiabatic. As a result, the temperature gradient is aligned with the x direction, and the heat flux, q, is determined by solving the steady-state heat conduction equation, given by

$$\nabla .\left(k\nabla T\right)=0,$$

(1)

where k is the thermal conductivity, which varies spatially throughout the domain to account for the underlying microstructure as illustrated in Figure 2. As in previous studies [9,20,21,22,23,24,25,26], we utilize the phase-field method to generate the distinct microstructures of the fuels. In this method, to distinguish between the fuel components, the phase-field variables ${\eta }_i$ are introduced such that their values indicate the type of region (e.g., matrix, second-phase particles, pores, or interfaces). Thermal conductivity is assigned accordingly, based on the local phase-field variable values. Moreover, as demonstrated in our earlier work [20], assigning a reduced thermal conductivity value at the interface is equivalent to assuming a specific interfacial thermal (Kapitza) resistance. The overall effective thermal conductivity is defined as

$$k_{eff}={\displaystyle \frac{q\times L}{T_r-T_l}}$$

(2)

Here, q is the average heat flux, T_r and T_l are the temperatures at the right and left boundaries, respectively, and L is the width of the simulation domain. (see Figure 2). We have previously utilized this approach for UO2-BeO [9] and U-Zr fuels [15]. For completeness, we present it here for the case of UO2-Mo fuels.

2.2.2. Microstructure Representation

The continuous microstructure was obtained by constructing Voronoi diagrams using multiple phase-field variables, following the approach used in phase-field models of grain growth in polycrystalline materials [9,15,16,17,18,19,20]. As in our work on UO2-BeO fuels [9], UO2 is represented as the second-phase particles (e.g., the red bulk grains in Figure 2), while Mo is represented as the matrix (the blue, diffuse grain boundaries in Figure 2), meaning it serves as the continuous phase. Note that the selection of the matrix and second phase in these models is arbitrary. It is typically assigned based on either volume fractions or phase continuity; here, we adopt the latter definition. The phase-field variable ${\eta }_i$ will take a value 1 inside each grain i (a UO2 s phase particle) and value 0 outside the grain/particle i. ${\eta }_i$ takes a value between 0 and 1 in the matrix (Mo). It is noteworthy to mention here that the interface regions were treated as autonomous regions with their own thermal properties. This approach was developed in [20] to account for the thermal resistance of the interfaces (Kapitza resistance). As we discussed in [15,20], the simplest way to assign thermal resistance to a diffuse interface is to express its thermal conductivity as a polynomial function of the bulk conductivities of the bordering phases and temperature. This is described here for UO2-Mo fuels as follows:

$$K(T,{\eta }_i) = \{ K_{UO2}(T), { \eta }_i=1;$$

$$K_{int}(T)=\left({\displaystyle \frac{K_{MO}\left(T\right)-K_{UO2}(T)}{2}}+K_{UO2}(T)\right)\left(x T^y+z\right), 0<{\eta }_i<0.1 or 0.9<{\eta }_i<1;$$

$$K_{MO}\left(T\right), 0.1 \le {\eta }_i \le 0.9 \}.$$

(3)

For the simulated 2D microstructures presented in this work, the domain size was set to 2048 nm × 2048 nm. As in our previous studies, the numerical implementation was carried out using the open-source MOOSE framework [21]. The microstructure features were allowed to relax for a few time steps to generate diffuse interfaces as discussed in our earlier work [9,15,20]. For the finite element mesh, QUAD4 elements with a size of 4 nm were used. The interface width was set to 2 nm, and three levels of mesh adaptivity were applied in this region to reduce the element size to 0.5 nm to ensure accurate representation of the interfacial thermal resistance. The volume fractions of Mo were also varied to compare the model predictions with available experimental results (UO2–2–5% Mo) [8] and later for testing the developed ML algorithms (See Section 2.3). Microstructures with different volume fractions were initiated by adjusting the area of the Mo phase, corresponding to the diffuse grain boundaries shown in Figure 2. The first set of simulations was designed to produce data aligned with the experimental parameters listed in Table 1. These data were used both to validate the physics-based models (Equations (1)–(3)) and to train the ML algorithms. The second set of simulations provided additional synthetic data for the testing stage of the ML algorithms.

Table 2. The parameters used in the physics-based simulations to generate synthetic data for the testing stage of the ML algorithms.

Fuel	Temperature Range (°C)	Increment (°C)	Used Compositions	Reference
UO2-BeO	25–300	25	7.5 and 12.5 (BeO Vol%)	[9]
UO2-Mo	300–1200	100	8 and 12 (Mo Vol%)	Current work
U-Zr	40–300	10	75 and 80 (TD *%)	[10,15]

* TD: theoretical density.

lists the parameters utilized in this second set of simulations. By comparing Table 1 and Table 2, we can observe that they share the same temperature range and increment but differ in their compositions.

2.3. Constructing ML Models of Thermal Conductivity

In general, regression, classification, and anomaly detection methods are widely used in supervised learning algorithms. Since the main target here is to predict the effective thermal conductivity, this work utilizes regression algorithms. To build any ML model, five main steps should be implemented as schematically illustrated in Figure 3.

2.3.1. Data Collection

The input data can be obtained from various sources such as computational methods or experimental studies. In the current work, the training stages were conducted based on experimental data (Table 1), while the testing stages were executed by using results of the validated mesoscale models. Specifically, the experimental datasets for UO2-BeO, UO2-Mo composite nuclear fuels, and U-Zr metallic fuel were obtained from [6,8,9]. The mesoscale model developed in this work was first validated (see Section 3.1) and then used to generate new datasets for the testing stage of the UO2-Mo fuel case. Previously validated mesoscale models [9,15] were used for the same purpose in the cases of UO2-BeO composite and U-Zr metallic nuclear fuels.

2.3.2. Data Preparation

Data preparation is an essential step in developing any ML model because careful preparation of data leads to significant improvement in model predictions. For instance, sometimes the datasets include invalid values, or some data are missing. In the case of missing values, the algorithm cannot be executed. Moreover, the invalid data will reduce the accuracy of the model.

2.3.3. Data Splitting

Traditionally, available data is split between the training and testing stages while constructing the ML algorithms. The common strategy is that 80% of the data is reserved for training while the remaining 20% is for testing. Since our physics-based, mesoscale models of the effective conductivity (Equations (1)–(3)) were experimentally validated first, they can be used to generate further data points as explained above. Therefore, we can utilize the complete original sets of experimental data for training only, which improves the ML algorithm’s accuracy. The synthetic data from simulations are then employed for testing. This was consistently conducted for the same temperature range and composition ratios used to obtain the experimental data (Table 1). An illustration of this novel approach for designing ML algorithms is presented in Figure 4, in comparison to Figure 3.

2.3.4. Choosing the Optimal ML Algorithm

Various supervised learning algorithms were explored in this study. We briefly review here the three most commonly used regression algorithms, e.g., Bayesian ridge, random forest, and multi-polynomial algorithms [22]. The first two were implemented natively in Python’s scikit-learn library, version 1.1.0. The multivariate algorithm was coded in MATLAB, version R2022a. Based on the testing stage, the performance of each algorithm is evaluated, and the optimal model is determined (see Figure 4).

Ridge regression addresses overfitting in linear models, which is common under multicollinearity or high-dimensional settings, by shrinking coefficients toward zero, improving stability and predictive performance at the cost of a small bias. Casting the linear model in a Bayesian framework yields posterior distributions for the weights and predictions; the Bayesian ridge makes this explicit by using Gaussian priors and estimating the regularization strength from the data via marginal-likelihood maximization, providing coherent uncertainty quantification alongside regularization.

For flexible nonlinear structure, we employ Random Forests and multi-polynomial regression. Random Forests aggregate many decorrelated decision trees trained on bootstrap samples with feature subsampling, delivering strong generalization, resilience to missing/heterogeneous inputs, and interpretable variable importance. Multi-polynomial regression captures smooth nonlinearities and interactions among variables (e.g., temperature and composition) in a transparent functional form but requires careful term selection or regularization to avoid overfitting as polynomial order grows. Together, these methods span a bias–variance spectrum and enable both accurate prediction and interpretability for thermal-conductivity modeling.

2.3.5. Model Evaluation

Model selection was based on a concurrent evaluation of predictive accuracy and linear association between predictions and observations. We report the root-mean-square error (RMSE) as an absolute accuracy metric: lower RMSE indicates that model predictions track the measured values more closely, penalizing large deviations more heavily due to the squaring of residuals. RMSE is computed over the non-missing data and provides an interpretable scale in the same units as the response variable.

Complementing RMSE, we use Pearson’s correlation coefficient (r) to quantify the strength of the linear relationship between predicted and observed responses. Values of r approaching +1 indicate a strong positive linear association, whereas values farther from unity reflect weaker alignment. Together, RMSE and r provide a balanced assessment: RMSE captures the magnitude of errors, and r captures relational fidelity, enabling the identification of the most reliable model among the candidates.

3. Results

As was discussed in Section 2, the physics-based mesoscale models were first developed and validated for distinct forms of nuclear fuels as detailed in our earlier works [9,15,25]. First, we present here, for completeness, the results of the microstructure-informed FEM simulations for the case of UO2- Mo fuels. We also discuss their validation based on the available experimental data. Lastly, we elaborate on the training, testing, and utilization of ML algorithms to efficiently predict the effective thermal conductivity of UO2- Mo, UO2-BeO, and U-10Zr fuels.

3.1. Validated Mesoscale Model of the Effective Conductivity of UO2-Mo Fuels

To obtain accurate predictions, realistic microstructures were generated in MOOSE, as detailed in Section 2. As described in Equation (3), the thermal conductivity of the composite is modeled by assigning the thermal conductivity of UO2 within grains, that of Mo in the intergranular regions, and a reduced value at interfaces to simulate interfacial thermal resistance (Kapitza resistance). The values of interfacial conductivity were obtained directly from Equation 3.

Similar to earlier studies on UO2-Mo composite fuels [8], initial predictions overestimated the experimental thermal conductivity. For the 5 vol.% Mo case (Figure 5), the model overpredicted the values by approximately 13.8–17%, depending on temperature. In the 10 vol.% case, the discrepancy increased to 38–41%. For both compositions, the overprediction was lowest at lower temperatures and increased with temperature, peaking at 1200 °C (17% for the 5 vol.% case and 41% for the 10 vol.% case). The near-identical increase (3%) in error for both cases suggests that the effect of temperature on interfacial resistance is consistent across compositions, assuming identical interfacial composition. Upon incorporating the Kapitza resistance, the model predictions were significantly improved. For the 5 vol.% Mo case, the average reduction in effective thermal conductivity across the temperature range was 17.7%, while the 10 vol.% Mo case showed a 29.5% reduction. This greater reduction in the higher Mo content case is attributed to the increased interfacial area, which amplifies the influence of interfacial resistance. The agreement with experimental data improved substantially with the inclusion of interfacial resistance. For the 5 vol.% Mo case, the deviation decreased from 13.8–17% to 1.9–4.7%, and for the 10 vol.% case, from 38–41% to 0.3–1.2%.

We have implemented the exact procedure presented above for predicting the effective thermal conductivity in UO2-BeO [9] and U-10Zr fuels [9]. Those experimentally validated models can then be utilized to generate reliable synthetic data for the testing and validation of ML algorithms. We next discuss both the training of ML algorithms based on experimental data along with the selection of ML algorithms based on the results of the validated high-fidelity simulations.

3.2. Training of the ML Algorithms

Three supervised machine-learning (ML) algorithms, namely Bayesian Ridge, Random Forest, and Multi-Polynomial Regression, were trained using experimental data corresponding to UO2-BeO, UO2-Mo composites, and U-Zr metallic fuels. Recall that we exclusively preserved the experimental data for training the ML algorithms and no results from the high-fidelity simulations were used in this stage. The training results are presented in Figure 6.

For the UO2-BeO system, the Bayesian Ridge and Random Forest algorithms yielded root-mean-square error (RMSE) values of 30% and 7.5%, respectively, whereas the Multi-Polynomial Regression achieved a significantly lower RMSE of 1.6%. In the case of the UO2-Mo composite fuel, the Bayesian Ridge and Random Forest models produced RMSEs of 27% and 11%, respectively, compared to 4.4% for the multi-polynomial model. For the U-Zr metallic fuel, the corresponding RMSEs were 39.5% (Bayesian Ridge), 6.7% (Random Forest), and 6.0% (multi-polynomial). Based on these training outcomes, the Bayesian Ridge algorithm was excluded from further analysis, and the Random Forest and Multi-Polynomial models were selected for testing.

3.3. Selection of the Best-Performing ML Algorithm

Unlike traditional ML workflows that allocate 20% of experimental data for testing, our approach leverages data generated by validated mesoscale simulations. This enables the full use of experimental data for training, enhancing model performance while avoiding reliance on costly experiments. New datasets were generated using mesoscale models for UO2-Mo (this work), UO2-BeO [9], and U-Zr [15], ensuring that testing data did not replicate any feature values from the training data. For instance, the temperature range was held constant while fuel compositions varied, as can be verified by comparing Table 1 and Table 2.

As shown in Figure 7, the maximum deviation between the Random Forest model and the mesoscale simulation results was 74% for UO2-BeO, 38% for UO2-Mo, and 34% for U-10Zr, indicating that the Random Forest algorithm is unsuitable for predictive purposes in this context. This is consistent with the known limitation of Random Forests in regression tasks, where their performance is generally inferior to classification problems [22]. In contrast, the multi-polynomial model exhibited significantly lower maximum errors: 10% for UO2-BeO, 7% for UO2-Mo, and 9% for U-10Zr. These results establish the multi-polynomial model as the most appropriate candidate for the prediction stage. Moreover, considering that the maximum deviation between the mesoscale physics-based models and corresponding experimental data was previously reported as 6% for UO2-BeO [9], 4.7% for UO2-Mo, and 4.5% for U-10Zr [15], the accuracy of the multi-polynomial model is within an acceptable range. Therefore, the multi-polynomial algorithm is selected to predict the effective thermal conductivity across a range of temperatures and compositions for UO2-BeO, UO2-Mo composites, and U-10Zr metallic fuels.

3.4. Utilization of the Best-Performing ML Algorithm for Prediction

Finally, we leveraged the strength of the selected machine-learning model trained on the full set of available experimental data and validated against high-fidelity mesoscale simulations. The Multi-Polynomial Regression model was employed to predict effective thermal conductivity for previously unexplored conditions. We detail here the specification of this algorithm for completeness. This algorithm is constructed to compute the relationship between the dependent variable (thermal conductivity) with one or more independent variables (e.g., temperature and composition). The general formulation of a third-order multi-polynomial for two variables can be expressed as

$$y\left(x_1,x_2\right)={\beta }_0+{\beta }_1{x}_1+{\beta }_2{x}_2+{\beta }_3{x}_1^2+{\beta }_4{x}_1{x}_2+{\beta }_5{x}_2^2+{\beta }_6{x}_1^3+{\beta }_7{x_{2}x}_1^2+{\beta }_8{x_{1}x}_2^2+{\beta }_9{x}_2^3+\epsilon$$

(4)

where β₀, β₁, …, β₉ are the coefficients to be determined, x₁ represents the composition fraction variable, x₂ denotes the temperature, and ε is the residual error term. The values of those coefficients are given in

Table 3. Coefficients of the multi-polynomial regression for different fuels.

Coefficients	UO2-BeO	UO2-Mo	U-Zr
${\beta }_0$	7.9376	9.2994	−2.0244 × 103
${\beta }_1$	−3.9705	1.1542 × 101	7.891 × 103
${\beta }_2$	−1.7994 × 10−3	−1.3382 × 10−2	−3.6173 × 10−1
${\beta }_3$	2.1487 × 102	6.0197 × 101	−1.0195 × 104
${\beta }_4$	7.6194 × 10−3	3.4578 × 10−2	8.5781 × 10−1
${\beta }_5$	−3.124 × 10−5	9.2212 × 10−6	3.9649 × 10−5
${\beta }_6$	6.4571 × 101	1.0141 × 101	4.3932 × 103
${\beta }_7$	−3.3483 × 10−1	−1.9144 × 10−1	−5.1382 × 10−1
${\beta }_8$	4.9151 × 10−6	−4.9791 × 10−6	9.7753 × 10−5
${\beta }_9$	6.1718 × 10−8	−2.4434 × 10−9	−1.4888 × 10−7

.

This predictive stage enables rapid estimation of thermal conductivity across a broad range of temperatures and compositions for UO₂-BeO, UO₂-Mo, and U-10Zr nuclear fuel systems. Figure 8 illustrates representative results from these predictions. Specifically, Figure 8 (top) presents the predicted thermal conductivity of UO₂-BeO composite fuels with BeO volume fractions of 8%, 12%, 16%, and 20% over a temperature range of 40–400 °C. Figure 8 (middle) shows predictions for UO₂-Mo composites containing 3%, 6%, 8%, and 12% Mo over a wider temperature span of 40–1200 °C. Figure 8 (bottom) displays predicted values for U-10Zr metallic fuel at theoretical densities of 72%, 75%, 80%, and 85%, across the 40–400 °C range.

These results demonstrate the power and efficiency of the integrated hybrid framework. Whereas experimental campaigns to generate comparable data may require weeks and mesoscale simulations may take hours to days, the machine-learning model delivers predictions in a matter of seconds. This capability represents a significant advancement in the rapid evaluation and screening of candidate fuel compositions, reducing reliance on time- and resource-intensive methods while maintaining a high degree of accuracy. Furthermore, since the Multi-Polynomial Regression model provides a compact analytical formula for the effective conductivity, it can be easily incorporated into engineering-scale fuel performance codes, avoiding the extra cost associated with coupling micro- and macro-scale models concurrently [23,24,25].

4. Discussion

This study introduces an integrated, multi-fidelity modeling framework for accurately and efficiently predicting the effective thermal conductivity (ETC) of advanced nuclear fuels. The novel contribution lies in the synergistic combination of experimental measurements, high-fidelity mesoscale simulations, and machine-learning (ML) regression algorithms. By validating physics-based finite element models against experimental data and using them to generate synthetic datasets for ML testing, this approach circum- vents the traditional trade-offs between data scarcity, computational cost, and model generalizability. Notably, the framework was demonstrated across three distinct nuclear fuel systems: UO₂-BeO, UO₂-Mo, and U-10Zr.

The results reveal that the incorporation of interfacial thermal resistance (Kapitza resistance) is essential for bringing mesoscale simulation results into close agreement with experimental measurements, reducing error from as high as 41% to below 2% in some cases. Among the machine-learning techniques tested, the Multi-Polynomial Regression algorithm consistently outperformed Bayesian Ridge and Random Forest models, achieving RMSEs as low as 1.6–6% across the three fuel types. The trained multi-polynomial model was then used to predict ETC across extended composition and temperature ranges, demonstrating robust accuracy while enabling near-instantaneous property estimation.

The significance of this integrated modeling strategy is twofold. First, it establishes a high-throughput, data-efficient pipeline that leverages minimal experimental input to enable wide-ranging predictive capabilities. Second, it provides a compact analytical form of the effective thermal conductivity relationship, making the model highly portable and readily embeddable into engineering-scale fuel performance codes. The hybrid workflow effectively decouples the reliance on time-consuming simulations during design iterations and material screening, thereby accelerating development cycles for next-generation nuclear fuels.

Future research can extend this framework in several promising directions. Incorporating irradiation-induced microstructural evolution into the mesoscale simulations would enable predictions under in-reactor conditions [23,24,25,26]. Expanding the database to include other accident-tolerant fuel-cladding systems would further prove the generality and scalability of the approach. Moreover, exploring physics-informed neural networks as a complement or alternative to polynomial regression may further improve accuracy and interpretability in high-dimensional parametric spaces. Finally, coupling this model with transient thermal analyses could offer deeper insights into the dynamic performance of fuels during off-normal and accident scenarios [23,24,25].