• The Korean Journal of Rheology
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• v.10 no.4
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• pp.202-216
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• 1998

Improved version of previous 'Orthotropic' closure approximation, termed 'ORW' has been numerically developed using new homogeneous flow data. Previous 'Orthotropic' closure approximation, i.e., ORF or ORL showed non-physical oscillation for interaction coefficient $C_1$<0.001 at simple shear flow. It also shows non-physcial oscillation and under-prediction compared with 'Distribution Function Calculation' at non-homogeneous flow of center-gated disk. These phenomena are mainly due to the flow data of 'Distribution Function Calculation' which were used for least-square optimization. ORW obtained by fitting flow data of low interaction coefficient does not show non-physical oscillation and results in reasonably good behaviors at non-homogeneous flows as well as homogeneous flows. Fitting function forms have not been found to improve overall behaviors. It has been found that considering all the eigenvalues of orientation tensor (including the third eigenvalues) might end up with a better closure approximation than just considering the first and second eigenvalues. It is, however, very important and yet difficult to select appropriate function forms of eigenvalues. Numerical simulation including coupling and in-plane velocity gradient effects were performed for injection mold filing process with a film-gated strip and a center-gated disk using ORW and various other closure approximations for comparisons. Although ORW is in excellent agreement with 'Distribution Function Calculation', the predicted results seem to have consistent error in comparison with experimental data. The diffusivity term with constant interaction coefficient might have to be further investigated in order to accurately describe orientation states.

• Journal of KIISE:Software and Applications
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• v.30 no.3_4
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• pp.326-338
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• 2003

The objective of a neural network design and model selection is to construct an optimal network with a good generalization performance. However, training data include noises, and the number of training data is not sufficient, which results in the difference between the true probability distribution and the empirical one. The difference makes the teaming parameters to over-fit only to training data and to deviate from the true distribution of data, which is called the overfitting phenomenon. The overfilled neural network shows good approximations for the training data, but gives bad predictions to untrained new data. As the complexity of the neural network increases, this overfitting phenomenon also becomes more severe. In this paper, by taking statistical viewpoint, we proposed an integrative process for neural network design and model selection method in order to improve generalization performance. At first, by using the natural gradient learning with adaptive regularization, we try to obtain optimal parameters that are not overfilled to training data with fast convergence. By adopting the natural pruning to the obtained optimal parameters, we generate several candidates of network model with different sizes. Finally, we select an optimal model among candidate models based on the Bayesian Information Criteria. Through the computer simulation on benchmark problems, we confirm the generalization and structure optimization performance of the proposed integrative process of teaming and model selection.