Metamodeling complex systems using linear and nonlinear regression methods

Kartal, Elçin
Metamodeling is a very popular approach for the approximation of complex systems. Metamodeling techniques can be categorized according to the type of regression method employed as linear and nonlinear models. The Response Surface Methodology (RSM) is an example of linear regression. In classical RSM metamodels, parameters are estimated using the Least Squares (LS) Method. Robust regression techniques, such as Least Absolute Deviation (LAD) and M-regression, are also considered in this study due to the outliers existing in data sets. Artificial Neural Networks (ANN) and Multivariate Adaptive Regression Splines (MARS) are examples for non-linear regression technique. In this thesis these two nonlinear metamodeling techniques are constructed and their performances are compared with the performances of linear models.


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For the analysis of thermoacoustic (TA) devices, computational methods are commonly used. In the computational studies found in the literature, the flow domain has been modelled differently by different researchers. A common approach in modelling the flow domain is to truncate the computational domain around the stack, instead of modelling the whole resonator to save computational time. However, where to truncate the domain is not clear. In this study, we have investigated how the simulation results are aff...
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In this work, an evolutionary type global optimization method for identifying the stable geometries of atomic clusters is developed and applied to carbon clusters for testing purpose. Monte Carlo (MC) type local optimization is used between genetic algorithm (GA) steps together with a special Mutation operation designed for the Cluster geometry optimization problem. Cluster geometries and the corresponding potential energies for carbon obtained with this GA-MC hybrid method are compared with available resul...
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We present a Bayesian method for building scoring systems, which are linear models with coefficients that have very few significant digits. Usually the construction of scoring systems involve manual efforthumans invent the full scoring system without using data, or they choose how logistic regression coefficients should be scaled and rounded to produce a scoring system. These kinds of heuristics lead to suboptimal solutions. Our approach is different in that humans need only specify the prior over what the ...
Randomness properties of some vector sequences generated by multivariate polynomial iterations
Gürkan Balıkçıoğlu, Pınar; Diker Yücel, Melek; Department of Cryptography (2016)
We examine the randomness properties of the sequences generated by the multivariate polynomial iterations method proposed by Ostafe and Shparlinski, by using the six different choices of polynomials given by the same authors. Our analysis is based on two approaches: distributions of the periods and linear complexities of the produced vector sequences. We define the efficiency parameters, PE for “period efficiency” and LCE for “linear complexity efficiency”, so that the actual values of the period and linear com...
Neural network calibrated stochastic processes: forecasting financial assets
Giebel, Stefan; Rainer, Martin (Springer Science and Business Media LLC, 2013-03-01)
If a given dynamical process contains an inherently unpredictable component, it may be modeled as a stochastic process. Typical examples from financial markets are the dynamics of prices (e.g. prices of stocks or commodities) or fundamental rates (exchange rates etc.). The unknown future value of the corresponding stochastic process is usually estimated as the expected value under a suitable measure, which may be determined from distribution of past (historical) values. The predictive power of this estimati...
Citation Formats
E. Kartal, “Metamodeling complex systems using linear and nonlinear regression methods,” M.S. - Master of Science, Middle East Technical University, 2007.