Fast and accurate emulation of complex dynamic simulators

2025-03-26

AI Summary

To address the low simulation efficiency and difficulty in balancing accuracy for complex dynamic simulators governed by differential equations (e.g., Lotka–Volterra, Lorenz systems), this paper proposes a Chain Gaussian Process (Chain GP) surrogate modeling framework enabling one-step-ahead, analytically tractable time-series response prediction. The method introduces a novel chained covariance structure that permits closed-form posterior inference—eliminating the need for Monte Carlo approximation—and inherently incorporates external driving inputs, thereby enhancing both predictive accuracy and generalization. Implemented as an open-source R package, *dynemu*, published on CRAN, it achieves speedups of several-fold to over an order of magnitude across multiple benchmark dynamical systems while maintaining or improving prediction accuracy. Key contributions include: (i) an analytically solvable GP architecture tailored for dynamical systems; (ii) a one-step-ahead surrogate modeling framework specifically designed for dynamic simulation; and (iii) an efficient, reproducible, and publicly available implementation.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Cognitive Modeling & Cognitive Systems: Simulating Human Behavior
• Machine Learning: Matrix & Tensor Methods

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Web Mining and Content Analysis: Web data generation and simulation

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 extsf{R} package, extsf{dynemu}, implementing the one-step-ahead emulation approach, is available on extsf{CRAN}.

Problem

• Emulating complex dynamic simulators accurately and efficiently
• Solving computationally intractable posterior mean and variance calculations
• Extending method to systems with forcing inputs

Innovation

• GP-based emulation for dynamic simulators
• Exact computation of posterior statistics
• Extends to systems with forcing inputs