Learning symbolic models of dynamical systems through Kolmogorov–Arnold Networks (KANs) in centralized and distributed settings

Identifying an interpretable and tractable model is a crucial step for the analysis and control of dynamical systems. In this work, we employ the recently introduced Kolmogorov–Arnold Networks (KANs), a novel neural network architecture tailored for symbolic regression and interpretability, to learn symbolic models directly from data without any a priori knowledge of the observed dynamics. We then extend our result to the distributed case through federated learning introducing the FedKANs algorithm. FedKANs allows agents observing similar, but non-identical, systems to cooperate to learn more efficiently a symbolic model without the need to exchange any process data. To our knowledge, this represents the first distributed deep learning framework for symbolic regression in dynamical systems. Numerical simulations validate the proposed solutions in various settings, involving linear, nonlinear, discrete-time and continuous-time dynamics.