Workflow of the ML/SISSO-accelerated MSI degree evaluation on TM/In 2 O 3 -ZrO 2 substrate. The central focus of this study is to explore the metal-support interactions (MSI) between the metal species and the substrate in TM/In 2 O 3 -ZrO 2 catalysts, extracting data from theoretical calculations and employing machine learning (ML) and the SISSO methods to characterize the degree of MSI. Firstly, we select the CO 2 hydrogenation to methanol reaction as our research target. Subsequently, we conduct the density functional theory (DFT) calculations to investigate the formate pathway in defective In 2 O 3 -ZrO 2 models loaded with Cu, Ni, and Pd, extracting the activation energies of each respective rate-determining step as indicators for evaluating the reaction. Then, from an experimental and characterization perspective, we investigate the CO 2 conversion, methanol yield, and product selectivity at different temperatures, providing experimental evidence for our prior theoretical results. By combining computational and experimental data, we find a close correlation between the degree of MSI and the activation energy of the rate-determining steps, thus selecting activation energy as the target for prediction. Among a series of theoretical data, we select applicable thermodynamic features as potential descriptors and use scaling relations to identify two descriptors with high linear correlation, serving as the fundamental inputs for the SISSO method. Additionally, we attempt to incorporate all descriptors into ML methods for measurement and find that neural network (NN) method demonstrates the best predictive accuracy. In summary, this work provides a comprehensive approach spanning theoretical calculations, experimental validation and data analysis for MSI investigation, offering valuable analytical methods for CO 2 hydrogenation research. [Display omitted] • Methanol synthesis by CO 2 hydrogenation was studied by a multifaceted approach. • Ni-modified In 2 O 3 -ZrO 2 catalyst presented thermodynamic and kinetic superiority. • Two improvement strategies were proposed based on SISSO and ML methods. • An evaluation template for MSI degree between TM and carrier was established. Amidst the escalating concerns surrounding energy and environmental issues, the hydrotreatment of emitted CO 2 and conversion into C1 products, such as methanol, have emerged as a pivotal strategy for effective mitigation. Previous investigations have identified the potential of indium-zirconium oxide catalysts doped with transition metals (TMs) for methanol synthesis. However, a comprehensive understanding of the impact of different TM loadings on catalytic performance, as well as a quantitative elucidation of the degree of metal-support interaction (MSI) between TM and substrate, necessitates further exploration. A multifaceted approach covering density functional theory (DFT) calculation, experimental validation and machine learning (ML) analysis is employed in this study to elucidate the underlying principles of MSI influence on hydrogenation, culminating in two general models for predicting the activation energy representing the degree of MSI. Consistent findings from theoretical calculations and experimental results demonstrate that, in comparison to Cu and Pd, Ni doped In 2 O 3 -ZrO 2 catalyst shows superior performance both in thermodynamics and kinetics. This enhancement is attributed to the strong degree of MSI relationship between thermodynamically stable Ni and substrate, consequently leading to the enhancement in reducibility. Moreover, a three-layer framework is constructed to predict the activation energy in the formate pathway, which facilitates the evaluation of MSI degree in TM-loaded catalysts. To sum up, this work provides guidance for CO 2 hydrogenation studies and quantitative analysis of MSI, contributing to a heightened understanding of the interaction mechanisms in analogous research systems. [ABSTRACT FROM AUTHOR]