MLIPs often focus on regression metrics like Mean Absolute Error (MAE) or Root Mean Squared Error (RMSE) because the models deal with continuous energy or force values where R² may not fully capture physical accuracy. RMSE and MAE directly reflect prediction error magnitudes, which are more interpretable in materials science contexts.

Machine-learned atomic potentials predict energy and forces based on atomic configurations, which are inherently nonlinear and may involve complex interactions that do not fit neatly into a simple regression framework.

Machine-learned atomic potentials (MLIPs) are primarily useful for evaluating linear regression models, as they indicate the proportion of variance explained by the model. However, in the context of machine-learned atomic potentials, the focus is on the accuracy of energy and force predictions, making mean absolute errors and root mean square errors (RMSE) more important metrics. These metrics provide a direct measure of prediction error and are more suitable for evaluating the performance of models dealing with high-dimensional data and complex relationships in atomic systems.

You could correlate the predicted and the fitted data. Then you have your R-squared. Cor(y, y_hat)^2