## 2 Reaction Mechanisms and Kinetics of Electrocatalytic Nitrate Reduction
### Machine Learning and Artificial Intelligence for Efficient eNO\({}_{3}\)R  
For eNO\({}_{3}\)R, computational methods like DFT, molecular dynamics, and microkinetics have been invaluable in predicting catalyst behaviors and screening materials as discussed above. However, traditional atomistic simulations, while accurate, are computationally intensive, limiting their ability to explore large catalyst design spaces. Machine learning (ML) offers a solution by rapidly predicting catalyst performance using scaling relationships like Bronsted-Evans-Polanyi (BEP) and adsorption-energy trends. By leveraging data-driven approaches, ML can identify optimal catalytic properties for eNO\({}_{3}\)R [75]. As demonstrated by [PERSON] et al. [76] ML models like Gradient Boosting Regression (GBR) were trained using key intrinsic properties of transition metals--such as d-electron number, electronegativity, and atomic radius--to predict adsorption energies of nitrogen intermediates. This approach significantly reduced computational costs, offering reliable predictions for both side-on and end-on adsorption modes, with the potential to accelerate the discovery of highly efficient eNO\({}_{3}\)R catalysts. The model's interpretability further enhances the understanding of catalyst behavior, highlighting the role of ML in advancing catalytic design for nitrate  
Figure 8: Theoretical (**a**) and experimental (**b**) Faradaic efficiencies of different products for eNORR on Ag [73]. (**c**) Microkinetically modeled and (**d**) Experimentally measured potential-dependent nitrate order, measured by steady-state chronoamperometry in 0.1 M Na\({}_{x}\)H\({}_{3}\)-xPO\({}_{4}\) with a series of sodium nitrate concentrations for Cu (golden), Ni\({}_{0.68}\)Cu\({}_{0.32}\) (light blue), and Ni (orange) [74]. reduction [76]. In addition, a study by [PERSON] et al. [77] discovered that there was no linear correlation between the adsorption-free energies of reaction intermediates, making traditional free energy descriptors ineffective. For this reason, they employed Random Forest (RF) algorithm to predict the limiting potentials (U\({}_{\text{L}}\)) for electrocatalytic NO reduction (NORR) to NH\({}_{3}\), utilizing 22 atomic, electronic, and custom features. Through [PERSON]'s correlation, 11 key features were selected for further analysis, including atomic structure and bond lengths. The RF model demonstrated excellent performance with an R\({}^{2}\) value of 0.96 and low RMSE, highlighting important features such as bond length, atomic number, and d-band center in influencing U\({}_{\text{L}}\). Furthermore, they applied the SISSO approach (Sure Independence Screening and Sparsifying Operator) to derive a simplified mathematical expression that links U\({}_{\text{L}}\) to the key features, which aligned well with DFT predictions. As a result, Cu and Pt/Cu single-atom catalysts (SAACs) were identified as promising candidates for NORR to NH\({}_{3}\). [77]. Another study by [PERSON] et al. [78] applied multiple ML algorithms--SVR, GPR, LASSO, RFR, and XGBR--to further investigate the structure-activity relationship in NORR. A key component of this analysis involved the use of a normalized dataset, with a 10-fold cross-validation approach used to identify optimal hyperparameters for the ML models. The Random Forest Regression (RFR) and XGBR models outperformed others, demonstrating excellent generalization ability with R\({}^{2}\) values of 0.95 and 0.98, and RMSE values of 0.30 eV and 0.19 eV, respectively. These models provided reliable predictions of Gibbs free energy changes for the reaction intermediates [78]. Other models have been developed to improve the prediction of adsorption energies and active sites, such as the TinNet (Theory-Infused Neural Network) model and the Bayesian Statistical Learning model (Bayeschem).