Surrogate Models for Optimization of Dynamical Systems

TL;DR

This paper introduces a data-driven approach to create low-dimensional surrogate models for complex dynamical systems, significantly reducing computational costs in optimization tasks while maintaining accuracy and robustness.

Contribution

It proposes a novel surrogate modeling technique combining proper orthogonal decomposition and radial basis functions for efficient optimization of dynamical systems.

Findings

Surrogate models outperform variable order methods in computational time.

Models maintain accuracy with relative maximum absolute error measure.

Robustness demonstrated in nonlinear system scenarios.

Abstract

Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven mechanism to construct low dimensional surrogate models. These surrogate models reduce the computational time for solution of the complex optimization problems by using training instances derived from the evaluations of the true objective functions. The surrogate models are constructed using combination of proper orthogonal decomposition and radial basis functions and provides system responses by simple matrix multiplication. Using relative maximum absolute error as the measure of accuracy of approximation, it is shown surrogate models with latin hypercube sampling and spline radial basis functions dominate variable order methods in computational time of optimization, while preserving the accuracy. These surrogate models also show robustness in presence of model non-linearities. Therefore, these computational efficient predictive surrogate models are applicable in various fields, specifically to solve inverse problems and optimal control problems, some examples of which are demonstrated in this paper.