Data-driven simulation of forced nonlinear dynamical systems via multi-output Gaussian processes with intrinsic coregionalization

Nonparametric identification of forced nonlinear dynamical systems from noisy data remains a significant challenge, particularly when governing equations are unknown and states are coupled. This paper introduces MOGP_ICM-ODEs, a data-driven simulation framework based on a multi-output Gaussian process (MOGP) with an intrinsic coregionalization model (ICM) that jointly models all system states via a shared kernel structure. Exploiting the fact that differentiation is a linear operation on Gaussian processes, state derivatives are obtained analytically by differentiating the ICM kernel, eliminating the need for numerical differentiation. These derivatives are used to train a second MOGP_ICM surrogate that maps forcing inputs and system states to their temporal derivatives, enabling forward simulation under unseen excitation conditions without retraining. The framework is validated on a coupled nonlinear benchmark system and a continuous stirred-tank reactor (CSTR), and compared with five alternative identification methods. Across multiple noise levels and excitation frequencies, MOGP_ICM-ODEs gives accurate state and derivative estimates and attains the lowest error.