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 quite complicated and require a lot of hyperparameter tuning and computational resources. In this paper, we present our new method 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 powerful global optimizer, this approach results in an effective method to tackle the problem of SR. Furthermore, it can be easily extended to more advanced algorithms, e.g., by adding a deep neural network to find good-fitting parametric families. We prove the performance of ParFam with extensive numerical experiments based on the common SR benchmark suit SRBench, showing that we achieve state-of-the-art results. Our code and results can be found at https://github.com/Philipp238/parfam .

翻译：符号回归（SR）问题出现在许多不同的应用中，例如从给定数据中识别物理定律或推导描述金融市场行为的数学方程。解决SR问题的方法多种多样，通常基于遗传编程。然而，这些方法通常相当复杂，需要大量超参数调整和计算资源。在本文中，我们提出了新方法ParFam，它利用合适符号函数的参数族将离散的符号回归问题转化为连续问题，从而相比当前最先进的方法实现了更简洁的设置。结合强大的全局优化器，该方法成为解决SR问题的有效手段。此外，它可以轻松扩展至更高级的算法，例如通过添加深度神经网络来寻找拟合良好的参数族。我们基于常见符号回归基准套件SRBench进行了大量数值实验，证明了ParFam的性能，表明我们取得了最先进的结果。我们的代码和结果可在https://github.com/Philipp238/parfam获取。