Symbolic regression is an approach that searches the space of all possible mathematical equations to find an equation that minimizes some error metric for a given set of training data. Like other machine-learning regression approaches, the goal of symbolic regression is to leverage training data to build a model that generalizes well to test data. Although studied for several decades [5-7], symbolic regression has limited usage due to numerous challenges compared to other regression techniques. Most significantly, symbolic regression has an infinitely large search space due to the existence of infinite equations. In fact, not only is the search space infinite, but there are an infinite number of equations that coincide with any set of training data. As a result, the goal of symbolic regression is often not merely to find the equation with the least error, but also the simplest equation that minimizes the error, because a simpler equation tends to generalize better by minimizing overtraining.

Figure 6.   Multi-parameter modeling workflow using symbolic regression