An efficient parameter estimation method for nonlinear high-order systems via surrogate modeling and cuckoo search
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METHODOLOGIES AND APPLICATION
An efficient parameter estimation method for nonlinear high-order systems via surrogate modeling and cuckoo search Xuefang Lai1 · Xiaolong Wang1 · Yufeng Nie1
· Xingshi He2
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This work developed an efficient parameter estimation method for nonlinear high-order systems using surrogate modeling and cuckoo search. Specifically, to address the heavy computational burden required for evaluating the candidate parameters, we utilized a low-dimensional surrogate model to approximate the original system. The surrogate model was constructed by employing the proper orthogonal decomposition and the discrete empirical interpolation method. Then, to obtain the parameters of the original system, we applied the cuckoo search algorithm to solve the optimization problem that was built on the surrogate model. The accuracy and efficiency of the proposed method were verified on two numerical experiments, dealing with the identification of parameters for the FitzHugh–Nagumo system and the predator–prey system. The results showed that our approach yields accurate results while significantly reducing the computational cost. Keywords Parameter estimation · Nonlinear high-order systems · Surrogate model · Cuckoo search algorithm
1 Introduction Many physical, biomedical and control systems are mathematically modeled by parameterized nonlinear partial differential equations (PDEs). Due to the complexity and the unobservability of systems, model parameters usually are unknown and difficult to measure directly. Parameter estimation of the nonlinear PDEs is an essential issue in nonlinear science (Xun et al. 2013; Mücller and Timmer 2004; Boiger and Kaltenbacher 2015; Stefano et al. 2017; Chen et al. 2017). Based on surrogate modeling and meta-heuristic algorithm, we present an efficient parameter estimation method for nonlinear high-order dynamical systems, which arise from the discretization of nonlinear time-dependent PDEs. The parameter estimation of systems usually is regarded as an inverse problem: finding the parameter value by minimizing the differences between observations and predictions Communicated by V. Loia.
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Yufeng Nie [email protected]
1
Research Center for Computational Science, School of Science, Northwestern Polytechnical University, Xi’an 710129, China
2
School of Science, Xi’an Polytechnic University, Xi’an 710048, China
(Boiger and Kaltenbacher 2015; Tarantola 2005). So far, a variety of classical techniques for dealing with inverse problems have been developed, including the least-squares method (Mller and Timmer 2002), Bayesian approach (Xun et al. 2013; Cui et al. 2015; Lieberman et al. 2010; Stefano et al. 2017), wavelet multiscale method (Fu et al. 2013), the well-known regularization approach which is initially introduced by Tikhonov for the problems of ill-posed (Tihonov 1963), and so on. Although some well-posed inverse problems can be effectively solved, solving the inverse problems of complex systems rema
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