ParFam -- Symbolic Regression Based on Continuous Global Optimization

Symbolic regression (SR) describes the task of finding a symbolic function that accurately represents the connection between given input and output data. At the same time, the function should be as simple as possible to ensure robustness against noise and interpretability. This is of particular interest for applications where the aim is to (mathematically) analyze the resulting function afterward or get further insights into the process to ensure trustworthiness, for instance, in physical or chemical sciences (Quade et al., 2016; Angelis et al., 2023; Wang et al., 2019). The range of possible applications of SR is therefore vast, from predicting the dynamics of ecosystems (Chen et al., 2019), forecasting the solar power for energy production (Quade et al., 2016), estimating the development of financial markets (Liu and Guo, 2023), analyzing the stability of certain materials (He and Zhang, 2021) to planning optimal trajectories for robots (Oplatkova and Zelinka, 2007), to name but a few. Moreover, as Angelis et al. (2023) points out, the number of papers on SR has increased significantly in recent years, highlighting the relevance and research interest in this area. SR is a specific regression task in machine learning that aims to find an accurate model without any assumption by the user related to the specific data set.