Simple descriptor derived from symbolic regression accelerating the discovery of new perovskite catalysts

Abstract

Symbolic regression (SR) is an approach of interpretable machine learning for building mathematical formulas that best fit certain datasets. In this work, SR is used to guide the design of new oxide perovskite catalysts with improved oxygen evolution reaction (OER) activities. A simple descriptor, μ/t, where μ and t are the octahedral and tolerance factors, respectively, is identified, which accelerates the discovery of a series of new oxide perovskite catalysts with improved OER activity. We successfully synthesise five new oxide perovskites and characterise their OER activities. Remarkably, four of them, Cs_0.4La_0.6Mn_0.25Co_0.75O₃, Cs_0.3La_0.7NiO₃, SrNi_0.75Co_0.25O₃, and Sr_0.25Ba_0.75NiO₃, are among the oxide perovskite catalysts with the highest intrinsic activities. Our results demonstrate the potential of SR for accelerating the data-driven design and discovery of new materials with improved properties.

Fig. 1. Workflow diagram.

It contains four major parts: dataset generation (blue), SR (red), materials design and screening (green) and experimental verification (brown).

Fig. 2. Data collection and process.

a The landscape of all V_RHE data produced by experiments, including eighteen conventional and five new perovskites (totally twenty-three perovskites listed as ‘Materials index’ with sequence shown in Table 1). Each perovskite has been made four samples and each sample has been measured three times (totally twelve measurements listed as ‘No. of measurements’). For each measurement, we adopted V_RHE values at five current densities of 50 µA cm⁻², 5 mA cm⁻², 10 mA cm⁻², 15 mA cm⁻², and 20 mA cm⁻². The exact values of those data points are provided in Supplementary Data 1–5. b The flowchart of symbolic regression based on genetic programming (see more details of this flowchart and SR in Supplementary Information).

Fig. 3. Descriptor generation and performance.

a Pareto front of MAE vs. complexity of 8640 mathematical formulas shown via density plot. b V_RHE vs. μ/t (black diamonds: conventional perovskites; red dots: new perovskites). The current densities are normalised by BET surface areas (Supplementary Table 2) and loading amount. c Figure 2 from the study of Suntiviich et al. reproduced with permission from the American Association for the Advancement of Science. d Reformatted plot according to descriptor μ/t of c. The MAE (Pearson correlation coefficient) for c, d were 20.6 meV (0.923) and 21.0 meV (0.928), respectively.(The error bar in b is produced by the maximum and minimum values in experiments data).

Fig. 4. OER characterisations of Ba_0.5Sr_0.5Co_0.8Fe_0.2O₃ and predicted new oxide perovskites.

a LSV curves. b Corresponding Tafel slopes. c Mass and specific activities. d Results of stability tests under galvanostatic conditions at 10 mA cm⁻² disk current density.

Fig. 5. Morphology measurements of Ba_0.75Sr_0.25NiO₃ before and after OER testing.

a HRTEM before a stability test. b HRTEM after a stability test. Right side: STEM atomic mapping (scale bar: 500 nm). The labelled lattice spacing is around 0.3 nm, which corresponded to the (110) lattice planes of Ba_0.75Sr_0.25NiO₃, in good agreement with the PXRD measurements. The insets of a, b show the fast Fourier transform image of the corresponding HRTEM image. The well-regulated arrayed spots indicated that the grown crystal had high crystallinity. HRTEM of Ba_0.75Sr_0.25NiO₃ before and after OER testing clearly showed the same lattice spacing and very similar fast Fourier transform images, suggesting outstanding stability of the Ba_0.75Sr_0.25NiO₃ sample under OER conditions. The maintenance of good crystallinity indicates that Ba_0.75Sr_0.25NiO₃ is a stable OER electrocatalyst. In order to verify the atomic distribution, STEM mapping was conducted; the even distribution of the atoms over the analyzed area further demonstrates the excellent stability of the sample.