  The problem of symbolic regression (SR) arises in many different
applications, such as identifying physical laws or deriving mathematical
equations describing the behavior of financial markets from given data. Various
methods exist to address the problem of SR, often based on genetic programming.
However, these methods are usually complicated and involve various
hyperparameters. In this paper, we present our new approach ParFam that
utilizes parametric families of suitable symbolic functions to translate the
discrete symbolic regression problem into a continuous one, resulting in a more
straightforward setup compared to current state-of-the-art methods. In
combination with a global optimizer, this approach results in a highly
effective method to tackle the problem of SR. We theoretically analyze the
expressivity of ParFam and demonstrate its performance with extensive numerical
experiments based on the common SR benchmark suit SRBench, showing that we
achieve state-of-the-art results. Moreover, we present an extension
incorporating a pre-trained transformer network DL-ParFam to guide ParFam,
accelerating the optimization process by up to two magnitudes. Our code and
results can be found at https://github.com/Philipp238/parfam.
