KAN-SR: A Kolmogorov-Arnold Network Guided Symbolic Regression Framework

Abstract

We introduce a novel symbolic regression framework, namely KAN-SR, built on Kolmogorov Arnold Networks (KANs) which follows a divide-and-conquer approach. Symbolic regression searches for mathematical equations that best fit a given dataset and is commonly solved with genetic programming approaches. We show that by using deep learning techniques, more specific KANs, and combining them with simplification strategies such as translational symmetries and separabilities, we are able to recover ground-truth equations of the Feynman Symbolic Regression for Scientific Discovery (SRSD) dataset. Additionally, we show that by combining the proposed framework with neural controlled differential equations, we are able to model the dynamics of an in-silico bioprocess system precisely, opening the door for the dynamic modeling of other engineering systems.