KAN-SR: A Kolmogorov-Arnold Network Guided Symbolic Regression Framework
This addresses the problem of finding mathematical equations from data for scientific discovery and engineering modeling, representing an incremental improvement with a novel method.
The paper tackles symbolic regression by introducing KAN-SR, a framework based on Kolmogorov-Arnold Networks, which recovers ground-truth equations from the Feynman SRSD dataset and models bioprocess dynamics precisely.
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.