Using Machine, Essay On Inversion Of Radiate Transfer Equation Is Shortened.

Artificial Neural Networks and their architecture

Question:

Discuss about the Inversion Of Radiate Transfer Equation Using Machine.

The neural network approach is adopted from the biological to artificial neurons and it consists of dendrites, soma, axon, synapse, and the neuron activates after a certain threshold is met. The learning occurs through the electronic and chemical changes in the effectiveness of synaptic junction. An artificial neuron is simulated on hardware or by software. The input connections and the receives as well as the node, unit, or PE simulates neuron body, output connection as the transmit. The activation function employs a threshold or bias and the connection weights act as synaptic junctions.  Basic function of neuron is to sum inputs and produce output given sum is greater than threshold. ANN node produces an output as follows:

• Multiplies each component of the input pattern by the weight of its connection.
• Sums all weighted inputs and subtracts the threshold value implies total weighted input.
• Transforms the total weighted input into the output using the activation function.

The limitations of perceptron is the ability to form only linear discriminate functions such as the classes which can be divided by a line or hyper-plane. The most functions are more complex as they tend to be non-linear or not linearly separable. The combined results of two neurons can produce good classification. More complex multi-layer networks are needed to solve more difficult problems. In the multi-layer feed forward, Artificial Neural Networks have hidden layer of nodes allowed combinations of the linear functions. The non-linear activation functions displayed properties closer to real neurons where the output varies continuously but not linearly. The non-linear ANN classifier is possible. There was no learning algorithm to adjust the weights of a multilayer network and the weights have to be set. One of the most common ANN learning algorithm is the back propagation whose error is sent back through the network to correct all weights. Similarly, to the perceptron, the calculation of error here is based on the difference between the target and the yield. The back propagation is therefore, the rate of change of the error which is the most vital feedback through the network. The generalized delta rule relies on the sigmoid activation function for communication. The cell body performs a weighting algebraic sum or integration of the input signals. If the result exceeds a certain threshold value then the neuron becomes active and produces a potential action which is sent to the axon. If it does not exceed the threshold value, the neuron remains in idle state. An artificial neural network receives external signals on one input layer of nodes, each of which is connected with a number of internal nodes, organized in several levels. Each node processes the received signals and transmits the result to succeeding nodes. An artificial neuron is the fundamental calculus unit of the neural network and in the neural model it is formed from three basic elements.

Applications of multi-layer feed-forward artificial neural networks (ANN) to spectroscopy are reviewed. Network architecture and training algorithms are discussed. Back-propagation, the most commonly used training algorithm, is analyzed in greater detail. The following types of applications are considered: data reduction by means of neural networks, pattern recognition, multivariate regression, robust regression, and handling of instrumental drifts (Cirovic).

Training algorithms for ANNs

In the linear optic, there is a transient phenomenon that has no effect on anything. In the transparent volume of a non-linear optical medium. The interference pattern causes a change in the refractive index of the non-linear medium in the shape of those same parallel planes. An optical perceptron with a soft optical threshold is implemented and trained with an adapted Back propagation algorithm. The optical thresholding perceptron is composed of two section named matrix-vector-multiplier and a thresholding device (Steck1, Skinner, Cruz-Cabrera, Yang, & Behrman).

In the early learning phase, the artificial neural network is presented with input data set and trained to fire out the desired values at the output layer. The training algorithm iteratively modifies weights on connections through which signals are transmitted in order to minimize the gap between network output and desired one. The autoencoder model is an auto associative neural network encoder or simply autoencoder has the auto associative feature and bottleneck layer. The learning algorithm for Neural Networks requires certain parameters such as the learning rate, momentum, type of activation function of each neuron, error calculation function and the network topology to train and test. In this work, the first goal to achieve is to find a structure of adequate network while the optimization of the parameters remains a secondary aspect. In fact, considering the type of data and physical principles that characterize them, it is seen that spectra values are ranging in the intervals centered at 0 where there is the absence of scattering (Munshi, Cummingham, Linfield , Davies, & Edwards, 2009).

The scalar input is multiplied with the scalar weight to form one of the terms that is sent to the summer. The other input is multiplied by a bias and then it is passed to the summer. The summer output, which is also referred to as the net input, goes into a transfer function which produces the scalar neuron output.

The neuron has a bias which is summed with the weighted inputs to form the net input and the neuron output. This first index indicates the particular neuron destination for that weight and the second index indicates the source of the signal fed to the neuron.

The layer includes the weight matrix, W, the summers, the bias vector, b, the transfer function boxes and the output vector a. each layer has its own weight matrix, its own bias vector, a net input vector and an output vector. The number of the layer as a superscript to the names for each of these variables. A layer whose output is the network output is the output layer and all the other layers tend to be hidden.

The main problem, in the quantitative analysis of turbid samples using near-infrared (NIR) spectroscopy, is that multivariate calibration models built on conventional spectroscopic measurements such as transmittance or reflectance are adversely affected by variations arising from multiple light scattering, because these variations are not necessarily related to changes
in chemical information, i.e., concentrations of chemical components.

The approach adopted for the transfer equation for the radiative theory is one to investigate the spectroscopy of the materials. Another approach that was adopted was the RTE-Based Scatter Correction and Calibration Approach. It was the proposed methodology for estimation of concentrations of chemical components in suspensions. The method involves

• Acquisition of the bulk optical properties
• Extraction of pertinent chemical information

The AD method is much faster but does not take into account beam width and assumes that the sample is of infinite width, thus ignoring any light loss through the sides of the sample which in some cases could lead to significant errors  (Dzhongava, Thennadil, & S, 2009).

• Simulated data from using radiative transfer theory
• MATLAB R2017b software

Note:

Wednesdays are for Supervisor Meetings and Supervisor Form filling.

The project budget as estimated for this project is $0 as supplied by the university for the entire work. It is crucial to note, however, that the Thesis proposal report does not attract any project costs.

The following items will be delivered at completion of the thesis project:

• Thesis Journal
• Supervisor meeting minutes
• Thesis Proposal Document
• Thesis Report
• Presentation Slides

The following materials will be utilized in the research process of the thesis design:

• The MATLAB R2017b Software
• Internet website and Peer-reviewed Journals
• The University Library
• The center for Neural Networks Machine Learning Website

References

Dzhongava, E. H., Thennadil, C. R., & S. N. (2009). Applied Spectroscopy. 25-32.

Raimundas, S., & Thennadil, S. (2009). Radiative Transient Equations Theory. Analytical Chemistry, 1-11.

Davis, A., and A. Marshak, Lévy kinetics in slab geometry: Scaling of transmission probability, in Fractal Frontiers, M. M. Novak and T. G. Dewey (eds.), World Scientific, Singapore, pp. 63-72 (1997).

Buldyrev, S. V., S. Havlin, A. Ya. Kazakov, M. G. E. da Luz, E. P. Raposo, H. E. Stanley, and G. M. Viswanathan, Average time spent by Lévy flights and walks on an interval with absorbing boundaries, Phys. Rev. E, 64, 41108-41118 (2001).

Davis, A. B., and A. Marshak, Photon propagation in heterogeneous optical media with spatial correlations: Enhanced mean-free-paths and wider-than-exponential free-path distributions, J. Quant. Spectrosc. Rad. Transf., 84, 3-34 (2004).

Davis, A. B., and H. W. Barker, Approximation methods in three-dimensional radiative transfer, in Three-Dimensional Radiative Transfer for Cloudy Atmospheres, A. Marshak and A. B. Davis (eds.), Springer-Verlag, Heidelberg (Germany), to appear (2004).

Buldyrev, S. V., S. Havlin, A. Ya. Kazakov, M. G. E. da Luz, E. P. Raposo, H. E. Stanley, and G. M. Viswanathan, 2001: Average time spent by Lévy flights and walks on an interval with absorbing boundaries, Phys. Rev. E, 64, 41108-41118.