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current quadratic approximation is good, we can achieve fast convergence to the minimum; otherwise, if the approximation is bad, we are at least guaranteed that initially f decreases along the Newton direction. Further details can be found in [79]. 3.3. Metamodels Metamodel is a low cost (and thus approximate) surrogate evaluation model, built using existing information, which can be used instead of the computationally expensive, exact evaluation tool. The cost of training a metamodel depends on its type and the training set size. Compared to the cost of an exact evaluation, that of training and using the metamodel is relatively low. Among the frequently used metamodels there are polynomial interpolation, artificial neural networks, gaussian processes, support vector machines. There are two ways of using the metamodels, the first called “off-line”, in which it is decoupled from the optimization loop, and the other called “on-line” in which the metamodels are trained during the optimization using updated information. In the following paragraphs the Artificial Neural Network, and a Method based on the Richardson Extrapolation will be described. 3.3.1. Artificial Neural Network GAs require evaluations of the fitness function for each individual in a generation, and this during several generations, until an optimal individual is selected: this is the major cause of their high computational cost. However, this drawback can be overcome if the fitness function is related to the design variables through an analytical expression. In order to reduce computational costs for viscous dense-gas flow optimization problems, the flow solver (actually viscous computations have been just done with SGS) and GA are coupled with an artificial neural network (ANN). ANN are non-linear statistical data-modeling tools, based on a biologic analogy. They can be used to model complex relationships between inputs and outputs or to find patterns in data. A very important feature of these networks is their adaptive nature, i.e. their capability of “learning”. This feature makes such computational models very appealing in application domains where one has little or incomplete understanding of the problem to be solved but where training data is readily available. ANN involve a network of simple processing elements (nodes or artificial neurons) which can exhibit complex global behavior, determined by the connections between the processing elements and element parameters. According to the choice of the 43PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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