Incorporating Background Knowledge in Symbolic Regression using a Computer Algebra System

Since John Koza pioneered the paradigm of programming by means of natural selection, many applications for SR in scientific discovery have emerged [1]. Unlike other applications of machine learning techniques, scientific research demands explanation and verification, both of which are made more feasible by the generation of human-interpretable mathematical models (as opposed to fitting a model with thousands of parameters) [2-4]. Furthermore, SR can be effective even with very small datasets ( 10 items) such as those produced by difficult or expensive experiments which are not easily repeated. The mathematical expressions produced by SR can easily be extrapolated to untested or otherwise unreachable domains within a dataset (such as extreme pressures or temperatures). For decades, SR has discovered interesting models from data in many applications including inferring process models at the Dow Chemical Company [5], rainfall-runoff modeling [6], and rediscovering equations for double-pendulum motion [7]. Symbolic regression has been applied across all scales of scientific investigation, including the atomistic (interatomic potentials [8]), macroscopic (computational fluid dynamics [9]), and cosmological (dark matter overdensity [10]) scales. Some techniques facilitate search through billions of candidate expressions, such as the space of nonlinear descriptors of material properties [11]. While most applications of SR in science focus on identifying empirical patterns in data, such "data-only" approaches do not account for potential insights from background theory. In fact, some SR works emphasize their capabilities of discovery "without any prior knowledge about physics, kinematics, or geometry" [7].