Learning Ecological and Epidemic Processes using Neural ODEs, Kolmogorov-Arnold Network ODEs and SINDy

TL;DR

The paper tackles learning intertwined ecological and epidemic dynamics by analyzing SIR, SIS, Lotka–Volterra, and the LVSIS eco-epidemiological model through three data-driven lenses: Neural ODEs, Kolmogorov–Arnold Network ODEs, and SINDy. It demonstrates that SINDy provides interpretable, sparse governing equations on clean data, while Neural ODEs and KANODEs offer flexible, robust learning—KANODEs in particular achieving comparable performance with far fewer parameters. Extending to spatio-temporal settings, the authors introduce a partial learning approach that fixes diffusion and learns hidden local couplings via neural closures, achieving accurate reconstructions in 1D and 2D domains. The work shows that combining data-driven discovery with known physics can enhance predictive capability for complex eco-epidemiological systems, while outlining limitations such as noise sensitivity for SINDy and computational costs for neural approaches, and proposing future directions toward multiscale, IMEX-based architectures.

Abstract

We consider epidemic and ecological models to investigate their coupled dynamics. Starting with the classical Susceptible-Infected-Recovered (SIR) model for basic epidemic behavior and the predator-prey (Lotka-Volterra, LV) system for ecological interactions, we then combine these frameworks into a coupled Lotka-Volterra-Susceptible-Infected-Susceptible (LVSIS) model. The resulting system consists of four differential equations describing the evolution of susceptible and infected prey and predator populations, incorporating ecological interactions, disease transmission, and spatial dispersal. To learn the underlying dynamics directly from data, we employ several data-driven modeling frameworks: Neural Ordinary Differential Equations (Neural ODEs), Kolmogorov-Arnold Network Ordinary Differential Equations (KANODEs), and Sparse Identification of Nonlinear Dynamics (SINDy). Numerical experiments based on synthetic data are conducted to investigate the learning ability of these models in capturing the epidemic and ecological behavior. We further extend our approach to spatio-temporal models, aiming to uncover hidden local couplings.

Figures (9)

• Figure 1: SIR: Comparison of prediction performance
• Figure 2: LV: Comparison of prediction performance
• Figure 3: LVSIS: Comparison of prediction performance
• Figure 4: SIR: Comparison of prediction performance. Noised data
• Figure 5: LV: Comparison of prediction performance. Noised data