ParFam - Symbolic Regression Based on Continuous Global Optimization

Philipp Scholl, Katharina Bieker, Hillary Hauger, Gitta Kutyniok

Primary Area: general machine learning (i.e., none of the above)

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Keywords: symbolic regression, global optimization, deep learning

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TL;DR: We introduce the symbolic regression method ParFam, which achieves state-of-the-art by leveraging the structure of common physical laws, and show how to extend ParFam to improve the performance further using deep learning.

Abstract:

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 can be found at https://anonymous.4open.science/r/parfam-90FC/README.md.

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Submission Number: 5667