Proteins can specifically bind to curved membranes through curvature-induced hydrophobic lipid packing defects. The chemical diversity among such curvature "sensors" challenges our understanding of how they differ from general membrane "binders" that bind without curvature selectivity. Here, we combine an evolutionary algorithm with coarse-grained molecular dynamics simulations (Evo-MD) to resolve the peptide sequences that optimally recognize the curvature of lipid membranes. We subsequently demonstrate how a synergy between Evo-MD and a neural network (NN) can enhance the identification and discovery of curvature sensing peptides and proteins. To this aim, we benchmark a physics-trained NN model against experimental data and show that we can correctly identify known sensors and binders. We illustrate that sensing and binding are phenomena that lie on the same thermodynamic continuum, with only subtle but explainable differences in membrane binding free energy, consistent with the serendipitous discovery of sensors.