Meta-Model Framework for Surrogate-Based Parameter Estimation in Dynamical Systems

Abstract: The central task in modeling complex dynamical systems is parameter estimation. This task involves numerous evaluations of a computationally expensive objective function. Surrogate-based optimization introduces a computationally efficient predictive model that approximates the value of the objective function. The standard approach involves learning a surrogate from training examples that correspond to past evaluations of the objective function. Current surrogate-based optimization methods use static, predefined substitution strategies that decide when to use the surrogate and when the true objective. We introduce a meta-model framework where the substitution strategy is dynamically adapted to the solution space of the given optimization problem. The meta model encapsulates the objective function, the surrogate model and the model of the substitution strategy, as well as components for learning them. The framework can be seamlessly coupled with an arbitrary optimization algorithm without any modification: it replaces the objective function and autonomously decides how to evaluate a given candidate solution. We test the utility of the framework on three tasks of estimating parameters of real-world models of dynamical systems. The results show that the meta model significantly improves the efficiency of optimization, reducing the total number of evaluations of the objective function up to an average of 77%.