Abstract
<jats:p> High-throughput experimentation (HTE) and machine learning (ML) have accelerated discovery in molecular chemistry. Meanwhile, such advances in heterogeneous catalysis are hindered by complex surfaces and vast chemical space. We present a mathematically optimized methodology using Steiner coverings to explore multi-component catalysts and access lower-dimension interactions through higher-dimension blocks. From 21 elements, we designed a library of 70 trimetallic mixed-metaloxide catalysts, covering all 210 possible bimetallic pairs. The experimental workflow was automated by a robotic platform and applied to thermocatalytic CO <jats:sub>2</jats:sub> hydrogenation, critical for achieving a circular carbon economy. In just 70 materials we successfully recovered established benchmarks for methanation, reverse water–gas shift (RWGS), and methanol synthesis, while discovering a highly active FeGaRu catalyst for CO <jats:sub>2</jats:sub> –Fischer–Tropsch synthesis that retains this activity when simplified to binary FeRu. Our combinatorial optimization methodology replaces thousands of manual experiments with strategic exploration, improving the discovery rate for complex, multi-component heterogeneous catalysts. </jats:p>