Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2021 001

Surrogate Models for Optimization of Dynamical Systems

Kainat Khowaja
Mykhaylo Shcherbatyy
Wolfgang Karl Härdle

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.

Keywords:
Proper Orthogonal Decomposition, SVD, Radial Basis Functions, Optimization,
Surrogate Models, Smart Data Analytics, Parameter Estimation

JEL Classification:
C00