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Surrogate Models for Optimization of Dynamical Systems

Kainat Khowaja, Mykhaylo Shcherbatyy and Wolfgang Härdle ()

No 2021-001, IRTG 1792 Discussion Papers from Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series"

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 (search for similar items in EconPapers)
JEL-codes: C00 (search for similar items in EconPapers)
Date: 2021
New Economics Papers: this item is included in nep-cmp and nep-ore
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