Proportionality Graphs, Units Analysis, and Domain Constraints: Improving the Power and Efficiency of the Scientific Discovery Process

An important subproblem of scientific discovery is quantitative discovery, finding formulas that relate some set (or subset) of a collection of numerical parameters. Current work in quantitative discovery suffers from a lack of efficiency and generality. This paper discusses methods that are efficient and yet general for discovering equations which try to avoid exponential search. Importantly, these methods can derive equations that cover subsets of the data and derive explicit descriptions of when the equations are applicable. These methods are fully implemented in a system named ABACUS which is described and some of its results are presented.