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Comparing and Demonstrating After both the models were trained, the performance of the trained shallow neural network and LSTM model was evaluated using the following decision matrix shown in Table 1 below Table 1: Evaluation of the Best LSTM and Shallow Neural Network Models Trained and Tested using Foreign Data The error values shown above were extracted from the best performing LSTM and shallow neural network models. It can be seen that the LSTM model performs better in terms of how accurately it plots the forecasted capacitance values to the actual values for different training and testing sets. Note that not only did the best performing LSTM model outweigh the performance of the shallow neural network, it is also important to observe how the models performed when compared to the worst results obtained form both the trained models Table 2: Evaluation of the Worst LSTM and Shallow Neural Network Models Trained and Tested using Foreign Data As seen form the RMSE recorded values for...
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Training the Long Short-Term Memory Model (LSTM) LSTM is a type of recurrent neural network (RNN) architecture that is particularly effective in processing and predicting sequences of data. LSTM networks are designed to address the limitations of traditional RNNs, which tend to struggle with capturing long-term dependencies in sequential data [1]. LSTMs were introduced by Hochreiter and Schmidhuber in 1997 as an enhancement to RNNs. The key innovation of LSTM networks is the incorporation of a memory cell, which allows them to selectively remember or forget information over extended time periods [2]. This memory cell is equipped with various gating mechanisms that regulate the flow of information, making it capable of capturing and preserving relevant information while disregarding irrelevant or redundant information. LSTM models are quite suitable for regression problems with time series data specially where forecasting comes into place. The models are a type of RNN (Recurrent Neu...
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Training the Shallow Neural Network

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Training using the Lavenberg-Marquardt Backpropagation Algorithm   In mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least squares curve fitting [1]. This shallow neural network has 10 hidden layers.  Here's a step-by-step explanation of how the Levenberg-Marquardt backpropagation algorithm works: Initialization: Initialize the weights and biases of the neural network with small random values. Forward Propagation: Feed a training input through the network and compute the corresponding output using the current weights and biases. This involves propagating the input forward through each layer of the network, applying activation functions and computing the output of each neuron. Compute the error: Compare the computed output with the desired outp...
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