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We reconstruct the Hubble function from cosmic chronometers, supernovae, andbaryon acoustic oscillations compiled data sets via the Gaussian process (GP)method and use it to draw out Horndeski theories that are fully anchored onexpansion history data. In particular, we consider three well-establishedformalisms of Horndeski gravity which single out a potential through theexpansion data, namely: quintessence potential, designer Horndeski, andtailoring Horndeski. We discuss each method in detail and complement it withthe GP reconstructed Hubble function to obtain predictive constraints on thepotentials and the dark energy equation of state.

A data-driven Reconstruction of Horndeski gravity via the Gaussian processes