Kolmogorov-Arnold Networks for Dynamics (KANDy)

I’m happy to present KANDy — Kolmogorov-Arnold Networks for Dynamics — an innovative framework for equation discovery, and I would love any feedback from the dynamical systems community.

KANDy combines Kolmogorov-Arnold Networks (KANs) with sparse regression to discover governing equations. While sparse regression is limited to discovering equations from a library of symbols, KANDy addresses this limitation with a zero-depth, wide KAN-style architecture. Sparse regression approaches to equation discovery often struggle in a variety of contexts. As such, KANDy seeks to discover the interpretability of governing equations and the structure that accompanies them.

KANDy has been applied to both continuous and discrete dynamical systems. This includes the study of chaos and systems described using PDEs. Of note, KANDy has successfully preserved the topological structure of the Hopf fibration.

I also welcome your feedback if your research is in the fields of:

• Data-Driven Dynamical Systems
• Koopman methods
• symbolic regression
• interpretable ML for scientific discovery
• KANs and KAN-inspired architectures
• modeling chaotic dynamical systems and PDEs

Paper: https://arxiv.org/abs/2602.20413

What are your impressions? Do you think KAN-based architectures can advance the field of scientific model discovery, or do you think the issues of sparsity and library selection will continue to be the most important constraints in the field?