Cheby-KANs: Advanced Kolmogorov–Arnold Networks for Applying Geometric Deep Learning in Quantum Chemistry Applications

Abstract

In this work, we present an enhanced version of the Kolmogorov–Arnold network (KAN) algorithm, called Cheby-KAN, that offers a more efficient, more reliable, and faster alternative to conventional KANs. We integrated our algorithm with a geometric deep learning model (SchNet) to assess the effect of integrating KANs representation on geometric deep learning by combining domain knowledge of quantum chemistry and our new representation. We initially tested our model on benchmark datasets, then we integrated Cheby-KAN with SchNet to obtain an enhanced model, called Cheby-KAN-SchNet.We used Cheby-KAN-SchNet to predict six quantum properties of molecules, and compared our results against the original SchNet results and another model integrating SchNet with the original KANs using basis splines to give a fair and objective comparison of our model.We expected to obtain the benefits of the powerful KANs representation and to reduce the high time and computational costs of KANS. We applied the algorithm to quantum chemistry because quantum chemistry requires extremely high precision modeling of the system where error rates increase exponentially. Our algorithm outperformed the original KANs with B-splines in terms of both speed and accuracy, and outperformed Schnet in terms of accuracy and consistency. These results demonstrate the potential of Cheby-KAN in addressing the approximation of multi-variate and complex functions under high levels of uncertainty, while offering enhanced interpretability compared to traditional neural network models or KANs with B-splines.