Static neural network

O. D. Sanni, M. S. Wagner, D. G. Briggs, D. G. Castner and J. C. Vickerman, Classification of adsorbed protein static ToF SIMS spectra by principal component analysis and neural networks, Surface and Interface Analysis, 33, 715 728 (2002). 

Sanni et al. [98] used neural networks and PCA for classification of adsorbed protein static time-of-flight (TOP) SIMS spectra. 

Modeled relationships can take the form of a step response, impulse response, state-space representation, or a neural network (see Section 2.6.17). If a linear form is desired, the model is usually linearized around some operating point. Another option is to produce a series of linear models, each representing a specific operating condition (usually load level). The obtained model can be used for solving a static optimization problem to find out the optimal operating point. The "optimal" criterion can be user selectable. 

Let us have a look at the prediction of the mean molecular polarizability a , , by neural networks and RDF descriptors. can be calculated from additive contributions of the atomic static polarizability a of individual atoms i... 

Influenced by the mind of forward modeling problems, it is easily directed to adopt complicated model classes so as to capture various complex physical mechanisms. However, the more complicated the model class is utilized, the more uncertain parameters are normally induced unless extra mathematical constraints are imposed. In the former case, the model output may not necessarily be accurate even if the model well characterizes the physical system since the combination of the many small errors from each uncertain parameter can induce a large output error. In the latter case, it is possible that the extra constraints induce substantial errors. Therefore, it is important to use a proper model class for system identification purpose. In this chapter, the Bayesian model class selection approach is introduced and applied to select the most plausible/suitable class of mathematical models representing a static or dynamical (structural, mechanical, atmospheric,...) system (from some specified model classes) by using its response measurements. This approach has been shown to be promising in several research areas, such as artificial neural networks [164,297], structural dynamics and model updating [23], damage detection [150] and fracture mechanics [151], etc. 

The output is calculated in two steps first, the input and output signals are delayed to different degrees. Second a nonlinear aetivation fimetion /( ) (here a static neural network) estimates the output. In (Nelles 2001) a sigmoid fimetion is proposed for the nonlinear activation function, which is used in this eontext. Other fimetions for nonlinear dynamie modeling e.g. Ham-merstein models, Wiener models, neural or wavelet network are also possible. 

This chapter deals with robot navigation avoiding static and dynamic obstacles in the path of the mobile robot, planning the future path of the mobile robot with the help of Artificial Neural Networks (ANNs) and also accepting the speech conunands to traverse the directed path and accordingly to reach the destination. 

A schematic diagram of the neural network-based adaptive control technique is shown in Fig. 4.9. A neural network identification model is trained using a static backpropagation algorithm to generate p(fc + 1), given past values of y and u. The identification error is then used to update the weights of the neural identification model. The control error is used to update the... 

Since dissolution is a time-dependent process, the dynamic (recurrent) neural networks are the more appropriate tool for modeling this process. Consequently, the main conclusion of this approach [19] is the superiority of Elman neural networks in drug release prediction in comparison to static neural networks. 

If the process conditions vary over a wide range, there may be a need for a non-linear empirical model. In case of a dynamic non-linear model there are a few possibilities for developing such a model, for example a dynamic neural network or a dynamic fuzzy model. One could also develop a Wiener model, in which the process dynamics are represented by a hnear model, such as a state space model. The static characteristics of the process are then modeled by a polynomial, able to represent the non-linearity. 

Modeling and forecasting. Modeling involves training the neural network on input-output data, such that an existing relationship between input and output data are represented sufficiently accurate. The relationship can be either static, in which case usually a feed-forward network is used. It could also be that the relationship is dynamic, in this case usually a recurrent neural net is used. Numerous applications can be found in the literature in different application areas, such as waste water plant modeling, data reconciliation, and so forth, see for example Miller et al. (1997), Meert (1998), Zhao et al. (1999), Basak et al. (2000) and Veltri et al. (2002). 

The first example to be considered is a static function approximation. The MATLAB neural network toolbox (Mathworks, 2006) will be used. A two-layer feed-forward neural network, consisting of a hidden layer and output layer, will be trained to approximate the sum of two sine waves. The function can be described by ... 

Neural networks may be divided into static (or traditional) and dynamic types. Although both types solve the same sorts of problems, they do so in different ways. Static nenral networks do not change their strueture onee they have been created and operate on a fixed number of classes (e.g. types of dinosaurs). Dynamie neural networks can change their structure and can operate in an environment where the number of elasses is not fixed. Which type to use will depend on the problem that is to be solved. 

Learning involves thus designating the miiumum of the error function. For this purpose, we usually apply gradient methods (conjugate gradients), based on the Hessian matrix (Newton, Levenberg-Marquardt methods), or on approximation of the inverse of the Hessian matrix (quasi-Newton methods) [2]. The MLP neural network is sensu stricte a static model, but it is possible to introduce dynamics... 

Static Feed-Forward Neural Network (SFNN)... 

The architecture of the static three layers of feed-forward neural network is shown in Fig. 1. This model is trained with the process dynamic parameto s and measured quality at the same time interval. Therefore, it works as a static model. The output of SFNN is calculated according to... 

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