We apply a singular value decomposition to this matrix and visualize the data projected onto the two leading principal components; these components capture the low-dimensional structure of the EC and show that this is highly correlated with the HFE. These results confirm that the topology of the SAM affects the HFE and that such topology can be captured using the EC; moreover, we can see that the topology of the SAM changes continuously as we increase/decrease the HFE. We next develop a linear regression model by using the water density EC curves and hydrogen bonding network EC values ⟨χ(G ww )⟩ as model inputs. The model chosen is a linear support vector machine (SVM) model taken from the LIBSVM library. We train the linear model using a set of 40 simulations with precomputed HFE values via the INDUS method (400 samples). Once the model has been trained, we test its prediction accuracy on a completely separate set of 10 SAM simulations (100 subsampled points). Our goal is to accurately predict the true HFE (computed via INDUS) for this separate set of simulations. The regression results for both model training and model testing are shown in Figure . We see that the linear model is able to predict the HFE for the testing set of simulations with little error (RMSE = 6.4 k B T ). Moreover, we have found that this model improves the results of a previously-developed 2D-CNN (RMSE = 8.0 k B T ), and is similar in performance to a 3D-CNN model (RMSE = 5.9 k B T ). The computations required to both train and predict with the linear model are minimal compared to INDUS and to both machine learning models. Thus, this topological approach can be used in the analysis of high-throughput simulations or in screening for surfaces with optimal chemical or physical properties. We have also compared the results obtained using the EC with models trained on water density profiles that capture fluctuations in water density as a function of distance from the SAM surface. All details of this analysis are found in the supplementary information and code. The water density profile models have a large error (RMSE = 20 k B T ). This confirms previous results that water density profiles are unable to characterize surface hydrophobicity. This finding is also supported by existing results from the areas of stochastic geometry and statistical thermodynamics, which demonstrate that the EC can be used to distinguish molecular configurations and phase transitions that the density profiles and radial distribution functions cannot distinguish. The linear prediction model uses topological information obtained from both graph and manifold representations of the SAM. We have found that when either representation (density field or hydrogen bond network) is used independently for developing a model, the resulting prediction RMSE values increase. Removing the graph EC ⟨χ(G ww )⟩ increases the RMSE of the model to 7.7 k B T . Removing the manifold EC curve χ increases the RMSE to 18 k B T . These results indicate that spatial fluctuations in water density play a much larger role in characterizing hydration free energy, which is consistent with past studies of water density fluctuations. Moreover, we have found that such models lead to severe underprediction of HFE for amide-dodecanethiol simulations. This may be explained by the tendency for amide end groups to form substantial hydrogen bonds with other amide end groups rather than water, which is unique for the surfaces studied. This added complexity is captured effectively when combining topological information from both graph and manifold representations and highlights how such representations can provide complementary information.