While quantitative structure–property relations (QSPRs) have been developed successfully in multiple fields, catalyst synthesis affects structure and in turn performance, making simple QSPRs inadequate. Furthermore, catalysts often have multiple active sites preventing one from obtaining insights into structure–property relations. Here, we develop a data-driven quantitative synthesis–structure–property relation (QS2PRs) methodology to elucidate correlations between catalyst synthesis conditions, structural properties and observed performance and to provide fundamental insights into active sites and a systematic way to optimize practical catalysts. We demonstrate the approach to the synthesis of nitrogen-doped catalysts (NDCs) made via pyrolysis for the performance of the electrochemical hydrogen evolution reaction (HER), quantified by the onset potential and the current density. We determine crystallinity, nitrogen species type and fraction, surface area, and pore structure of the NDCs using XRD, XPS, and BET characterization. We demonstrated that an active learning-based optimization combined with various elementary machine learning tools (regression, principal component analysis, partial least squares) can efficiently identify optimum pyrolysis conditions to tune structural characteristics and performance with concomitant savings in materials and experimental time. Unlike previous reports on the importance of pyridinic or graphitic nitrogen, we discover that the electrochemical performance is not driven by a single catalyst property; rather, it arises from a multivariate influence of nitrogen dopants, pore structure and disorder in the NDC materials. Identification of active sites can help mechanistic understanding and further catalyst improvement.
