Rethinking catalysis with interpretable AI and materials genes: SISSO symbolic regression combined with partial-effects sensitivity analysis

It introduces and demonstrates an interpretable AI workflow that adds gradient-based partial-effects (PE) sensitivity analysis on top of a SISSO symbolic-regression model to identify the most influential materials genes among the descriptors of a catalytic function. SISSO had already been used to find descriptors in materials science and catalysis, but which genes appear in a model and how strongly each of them influences it are two different questions; this work defines PEs as partial derivatives of the model with respect to a single gene, rescales them by the training-set standard deviation into scaled partial effects (SPEs) that are directly comparable across genes with different units, and averages them over all data points to obtain global sensitivity scores. The method is stated with explicit mathematical definitions (the partial-derivative expression and the SPE normalization) and derivatives of the SISSO expressions are evaluated analytically with SymPy; global SPE values are reported for each gene on a training set of nine materials and 539 data points, e.g. 2.81 for the average d-band center, 0.75 for the surface hydrogen binding energy, and 0.23 for the mean particle diameter.

For ethylene selectivity in the selective hydrogenation of concentrated acetylene streams, SISSO selects eight genes out of twenty primary features to form a three-dimensional descriptor vector, and the model describes both the different materials and their evolution with time on stream. The SISSO model itself originates from a previous focused SISSO study; the new element here is that the PE analysis reveals the relative importance of these genes and provides a per-material physical picture rather than refitting the model. The dataset covers nine Pd-based bimetallic alloys (Pd1Ag1, Pd1Ag5, Pd1Ag9, Pd1Au1, Pd1Au5, Pd1Au9, Pd1Cu1, Pd1Cu5, Pd1Cu9) supported on high-surface-area α-Al2O3, tested at 10 bar and 150 °C with a C2H2:C2H4:H2 ratio of 1:1:5 and a weight hourly space velocity of 90 000 cm3 gcat−1 h−1; 539 selectivity data points span 0–400 min, and nested five-fold cross validation gives R = 2 and D = 3 with a mean test error of 0.105, below 25% of the standard deviation of the selectivity distribution across the entire dataset.

The sensitivity analysis indicates that adsorption-related processes dominate ethylene selectivity: the average d-band center is the most influential gene, followed by the surface and subsurface hydrogen binding energies, and the sign of the relationship between these genes and selectivity can change with material and time on stream. This is consistent with earlier work on the hydrogenation of diluted acetylene streams that emphasized the adsorption of π-bonded species and hydrogen, but the present analysis further shows that under concentrated acetylene streams these relationships can be directly or inversely proportional depending on the material, so adsorption properties can either favor or hinder selectivity. Global mean absolute SPE values are 0.15 for tOS, 0.12 for w_metal, 0.23 for Dµ, 0.16 for the subsurface carbon deformation energy, 0.75 for the hydrogen surface binding energy, 0.092 for the work-function change upon hydrogen adsorption, 2.81 for the average d-band center, and 0.42 for the subsurface hydrogen binding energy; for Pd1Cu9 the SPE of the d-band center is positive while that of the hydrogen surface binding energy is negative, and the difference grows with tOS.

The experimentally measured mean particle diameter appears as the fourth most influential gene, pointing to a structure-sensitivity effect that is more pronounced for copper-based materials. Structure sensitivity had previously been discussed in detail mainly for the hydrogenation of dienes; this work links it to a statistical description of ethylene selectivity in concentrated acetylene streams and stresses that measured primary features capture aspects that are hard to include in a theoretical description, such as a particle-size distribution influenced by alloy properties, metal–support interactions, synthesis conditions, and possibly changes under reaction conditions. Per-material SPEs show that the particle-size distribution impacts the copper-based materials, in particular Pd1Cu9 and Pd1Cu5, more strongly than the remaining materials, while the model is less sensitive to the (sub)surface carbon-related genes, tOS, w_metal, and the work-function change upon hydrogen adsorption, suggesting a low influence of (sub)surface carbon on ethylene selectivity for the systems studied here.

The results describe ethylene selectivity for supported palladium-based bimetallic alloy nanoparticles in the selective hydrogenation of concentrated acetylene streams (>14 vol%) at 10 bar and 150 °C under full conversion; their value lies in providing a gene-level ranking of influence and screening leads for closely related systems and in demonstrating how experimentally measured and DFT-calculated parameters can be merged into primary features. The authors also note that SISSO and the materials genes provide reliable descriptions only for materials and reaction conditions governed by the same underlying physical processes as the training set, so the applicability boundary is set by the physical processes covered by the training data rather than by the chemical formula itself.

A careful reader would still watch several points: many primary features are measured before reaction or computed by DFT-GGA on low-index model surfaces, whereas properties such as the particle-size distribution may change under reaction conditions; the training set contains only nine materials, so the stability of the gene-influence ranking over a broader materials space remains to be tested; the observation that the model is less sensitive to (sub)surface carbon-related genes differs from the role of carbides discussed for diluted acetylene streams, and the conditions under which each picture applies deserve clarification; and although the full text was read, the equations and figures appear as images, so exact expressions and per-point distributions should be checked against the original figures and supplementary material.