Fast and Accurate Emulation of Complex Dynamic Simulators

Dynamic simulators are computational models governed by differential equations that evolve over time. They are essential for scientific and engineering applications but remain challenging to emulate because of 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 provides exact and tractable computation of the posterior mean and variance, solving a problem previously considered computationally intractable and eliminating the need for expensive Monte Carlo approximations. This approach substantially reduces computation time while maintaining or improving predictive accuracy. Furthermore, the method naturally extends to systems with forcing inputs by incorporating them as additional variables within the GP framework. Numerical experiments on multiple dynamic systems demonstrate the efficiency and computational advantages of the proposed approach. An R package, dynemu, which implements the one-step-ahead emulation approach, is available on CRAN.