## 1 Introduction
[37] used extreme gradient boosting (XGBoost) and Gaussian process regression to study the impact of sonication on the thermal conductivity of functionalized multi-walled carbon nanotube nanofluids, finding that the XGBoost model outperformed other models in predicting enhanced dispersion characteristics and stability. Although supervised ML models perform reliably the task of predicting thermal conductivity, there are not yet any comparisons of these models when applied to predict thermal conductivity of EG-Al2O3 nanofluids. Despite the traditional supervised ML models, physics-informed machine learning (PIML) [38] leverages domain knowledge from mathematical physics to enhance predictions and analyses, particularly in contexts where data may be incomplete, uncertain, or high-dimensional. This approach integrates seamlessly with kernel-based and neural network-based regression methods, offering effective, simple, and meshless implementations that are especially powerful in tackling ill-posed and inverse problems. For instance, [PERSON] et al. [39] present a deep learning-based model for reconstructing space, temperature, and time-related thermal conductivity through measured temperature, achieving precise real-time inversion without commercial software. The model includes data generation with a physics-informed neural network (PINN), noise reduction via a U-net, and inversion using a nonlinear mapping module (NMM), offering a robust and efficient alternative to traditional methods. [PERSON] et al. [40] demonstrate the application of PINNs to efficiently and accurately solve the phonon Boltzmann transport equation for mesoscale heat transfer, which excels in handling ballistic-diffusive heat conduction. Although PINNs are capable of operating with minimal training data, they rely heavily on the quality and scope of input data. Their performance and accuracy are contingent on comprehensive and unbiased data coverage; any gaps or biases can significantly impact the model's generalization and precision. Additionally, training PINNs can be more complex and challenging compared to traditional NNs, as they require the minimization of both data discrepancies and the residuals of physical equations. This task becomes particularly demanding when dealing with highly nonlinear and multiscale physical problems. Furthermore, the successful application of PINNs depends on a thorough understanding of physical laws and the accurate mathematical representation of the problem at hand. In caseswhere there is insufficient understanding of the physical processes or the physical models are imprecise, PINNs may fail to deliver accurate predictions. As previously mentioned, the physical mechanisms behind the enhancement of the thermal conductivity of nanofluids and influencing parameters remain a topic of debate, which makes developing PINNs that can predict the thermal conductivity of nanofluids a quite challenging task. For most ML models developed for solving regression problems, one significant limitation is their 'black-box' nature, i.e., the model's internal workings cannot be easily interpreted. This lack of interpretability poses challenges for further optimizing engineering and experimental design. To address this issue, Shapley additive explanations (SHAP) is usually employed to interpret complex models by attributing the contribution of each feature to the prediction target [41]. By incorporating SHAP analysis, the practical utility and reliability of ML models in predicting the thermal conductivity of nanofluids can be significantly enhanced. For instance, [PERSON] et al. [42] employed SHAP values to interpret models developed for predicting the electrical conductivity (EC), viscosity (VST), and thermal conductivity (TC) of EGO-Mxene hybrid nanofluids. The SHAP analysis revealed that T had a more significant impact on the predictions of all three response variables compared to concentration. Accordingly, the use of SHAP analysis can enable a deeper understanding of how changes in features influence predictions.