By A. Sanguineti
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Additional resources for 200 Victorian Fretwork Designs: Borders, Panels, Medallions and Other Patterns
Gradient algorithms Generally, the optimization methods that are used in neural network learning are second-order methods (Newtonian and quasi-Newtonian). The convergence speed of first-order methods is not suﬃcient; second-order methods are more eﬃcient but need more computing resources. The Hessian straightforward computation has to be avoided since a high dimension of the parameter vector (the number of connection weights) is involved. Besides, we shall see that the gradient is computed with eﬃciency and speed using the layer architecture.
In other words, the problem is to resample the input space E from the input learning set which constitutes the original sample. Several algorithms are available. The simplest one develops the idea of the Parzen window. The bandwidth is uniform. In the first step, the more representative input locations are chosen. More precisely, at the k-th step, k input points are available and the best linear model is computed. Next, to select the (k + 1)-th center, we pick up the location of the worst approximated data.
2. Simplified physical models In this case, the idea is to simplify the physical model to obtain a model that is simple enough to be used in global multidisciplinary optimization, while maintaining the physical behavior. The simplest formulation is an analytical formula. For example, for aerodynamic coefficients, we can use a “polar” type formula connecting the drag coefficient to the lift coefficient: C x = C x 0 + kC z2 ; the polar coefficients can be interpolated using a mathematical scale model.