Integrating Kolmogorov-Arnold networks with ordinary differential equations for efficient, interpretable, and robust deep learning: Epidemiology of infectious diseases as a case study

Abstract

This study extends universal differential equation (UDE) frameworks by integrating the Kolmogorov-Arnold Network (KAN) with ordinary differential equations, referred to as KAN-UDE, to achieve efficient and interpretable deep learning. Our case study centers on the epidemiology of emerging infectious diseases. Compared to UDEs based on multi-layer perceptrons, training KAN-UDE models shows significantly improved fitting performance, as evidenced by a rapid and substantial reduction in loss. KAN-UDE models demonstrate accurate reconstruction of nonlinear functions under partial time-series training data, maintaining robustness to data sparsity. This approach enables an interpretable learning process, as KAN-UDE models were reconstructed as fully mechanistic models (RMMs). While KAN-UDE models exhibit lower robustness and accuracy when real-world data randomness is considered, RMMs predict epidemic trends robustly and accurately over much longer time windows, as KAN precisely reconstructs the mechanistic functions despite data randomness.