Fast and accurate emulation of complex dynamic simulators

Abstract: While dynamic simulators, which are computational models that evolve over time and are governed by differential equations, are essential in scientific and engineering applications, their emulation remains challenging due to the unpredictable behavior of complex systems. To address this challenge, this paper introduces a fast and accurate Gaussian Process (GP)-based emulation method for complex dynamic simulators. By integrating linked GPs into the one-step-ahead emulation framework, the proposed algorithm enables exact analytical computations of the posterior mean and variance, eliminating the need for computationally expensive Monte Carlo approximations. This significantly reduces computation time while maintaining or improving predictive accuracy. Furthermore, the method extends naturally to systems with forcing inputs by incorporating them as additional variables within the GP framework. Numerical experiments on the Lotka-Volterra model and the Lorenz system demonstrate the efficiency and computational advantages of the proposed approach. An \textsf{R} package, \textsf{dynemu}, implementing the one-step-ahead emulation approach, is available on \textsf{CRAN}.