Fig. 2: The scientific method with scientific discoveries made via classical methods, data-driven methods, or AI-Hilbert.

AI-Hilbert proposes scientific laws consistent with a body of background theory formally articulated as polynomial equalities, inequalities, and relevant data sources. This likely allows scientific discoveries to be made using fewer data points than state-of-the-art approaches, and for missing scientific axioms to be deduced via abductive reasoning as part of the scientific discovery process. On the other hand, existing approaches to scientific discovery propose laws that may be inconsistent with either background theory or existing data sources. Note that blue denotes components associated with logical theories, purple denotes components linked to data, yellow denotes hypothesis generation, green denotes hypothesis testing, orange denotes discovery reporting, white denotes hypothesis refinement, teal denotes evaluation of the discovery, dashed lines represent macro components and green lines represent the input of AI-Hilbert.