The final errors are 0.153 WSE for training and 0.205 WSE for validation.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n The testing analysis<\/a> aims to validate the generalization properties of the trained neural network.<\/p>\n In this case, we show the minimums, maximums, mean, and standard deviations of the absolute and percent errors of the neural network for the testing data.<\/p>\n As we can see, the average error is around 1%<\/b>.<\/p>\n Additionally, the error histogram displays the distribution of errors from the neural network on the test samples.<\/p>\n In general, we expect a normal distribution like this.<\/p>\n As we can observe, most of the errors are around 0<\/b>. Once we have tested the neural network’s generalization performance, we can save it for future use in the so-called model deployment<\/a> mode.<\/p>\n<\/section>\n5. Testing analysis<\/h2>\n
<\/p>\n
<\/p>\n
\n<\/p>\n<\/section>\n6. Model deployment<\/h2>\n
References<\/h2>\n
Contents<\/h3>\n\n- Application type<\/a>.<\/li>\n
- Data set<\/a>.<\/li>\n
- Neural network<\/a>.<\/li>\n
- Training strategy<\/a>.<\/li>\n
- Testing analysis<\/a>.<\/li>\n
- Model deployment<\/a>.<\/li>\n<\/ol>\n
This dataset was generated using HFSS software, with the radiation frequency set at 2.4 GHz, a frequency commonly used for Bluetooth and WLAN operations, which can be utilized to optimize the design and performance of patch antennas.<\/p>\n
1. Application type<\/h2>\n<\/section>\n
The predicted variable in this application is the coefficient of reflection, S11, for a patch antenna.<\/p>\n
Therefore, this is an approximation project.<\/p>\n
Optimizing the antenna design aims to achieve the lowest possible value for S11, signifying high power transmission and minimal reflection levels, employing artificial intelligence and machine learning.<\/p>\n\n2. Data set<\/h2>\n
This dataset features information on patch antennas, a type of microstrip antenna widely used in wireless communications.<\/p>\n
The dataset includes various dimensions and parameters of the antenna, including the operating frequency, dimensions of the patch and slots, and a measure of the antenna’s reflection coefficient. The data is organized into 8 clusters.<\/p>\n
Variables<\/h3>\n
The number of input variables<\/a>, or attributes for each sample, is 7. The target variable<\/a> is S11.<\/p>\nThe following list summarizes the variables’<\/a> information:<\/p>\n<\/section>\nAntenna Dimensions<\/strong><\/h4>\n\n- Length of patch (mm)<\/strong>: Length of the patch antenna.<\/li>\n
- Width of patch (mm)<\/strong>: Width of the patch antenna.<\/li>\n
- Area of patch (mm\u00b2)<\/strong>: Total area of the patch antenna.<\/li>\n<\/ul>\n
Slot Dimensions<\/strong><\/h4>\n\n- Slot length (mm)<\/strong>: Length of the antenna slots.<\/li>\n
- Slot width (mm)<\/strong>: Width of the antenna slots.<\/li>\n
- Slot area (mm\u00b2)<\/strong>: Total area of the antenna slots.<\/li>\n<\/ul>\n
Operating Parameters<\/strong><\/h4>\n\n- Frequency (GHz)<\/strong>: Operating frequency of the antenna.<\/li>\n
- Reflection coefficient S11 (dB)<\/strong>: The S11 parameter, representing the antenna\u2019s reflection coefficient in decibels.<\/li>\n<\/ul>\n
\nInstances<\/h3>\n
Each instance<\/a>\u00a0contains the input and target variables of a different patient.<\/p>\nThe data set is divided into training, validation, and testing subsets.<\/p>\n
Neural Designer automatically assigns 60% of the instances for training, 20% for selection, and 20% for testing.<\/p>\n
Correlations<\/h3>\n
The\u00a0input-target correlations<\/a> might indicate which factors have the most significant influence on the reflection coefficient<\/span>.
\n![](\"https:\/\/www.neuraldesigner.com\/images\/reflection_coefficient_s11_db)
\nHere, the most correlated variables with survival status are area_slot_mm2<\/b> and slot_length_mm<\/b>.<\/p>\n<\/section>\n\n3. Neural network<\/h2>\n
The next step is to set\u00a0up a\u00a0neural network<\/a> that represents<\/span> the approximation function.<\/p>\nFor this class of applications, the neural network consists of the following components:<\/p>\n
\n- Scaling layer<\/a>.<\/li>\n
- Perceptron layers<\/a>.<\/li>\n
- Unscaling layer<\/a>.<\/li>\n
- Bounding layer<\/a>.<\/li>\n<\/ul>\n
Scaling layer<\/h3>\n
The scaling layer<\/a> contains the statistics on the inputs calculated from the data file and the method for scaling the input variables.<\/p>\nHere, the minimum-maximum method<\/a> has been set. As we use 7 input variables, the scaling layer has 7 inputs.<\/p>\nDense layers<\/h3>\n
We use 2 dense layers here.<\/p>\n
The first dense layer has 7 inputs, 3 neurons, and a hyperbolic tangent activation function<\/a><\/p>\nThe second dense layer has 3 inputs, 1 neuron, and a linear activation function<\/a><\/p>\nUnscaling layer<\/h3>\n
The unscaling layer<\/a> contains the statistics of the output.<\/p>\nThe following figure is a graphical representation of this neural network.
\n![](\"https:\/\/www.neuraldesigner.com\/images\/Network_architecture_s11_db.png\")
<\/p>\n<\/section>\n
4. Training strategy<\/h2>\n
The fourth step is to set the training strategy<\/a>, which is composed of two terms:<\/p>\n\n- A loss index.<\/li>\n
- An optimization algorithm.<\/li>\n<\/ul>\n
Loss index<\/h3>\n
The loss index<\/a> is the weighted squared error<\/a> with L2 regularization<\/a>, the default loss index for binary classification applications.<\/p>\nWe can state the learning problem as finding a neural network that minimizes the loss index.<\/p>\n
That is a neural network that fits the data set (error term<\/a>) and does not oscillate (regularization term<\/a>).<\/p>\nOptimization algorithm<\/h3>\n
The optimization algorithm<\/a>\u00a0we use is the\u00a0quasi-Newton method<\/a>, which is also the standard approach<\/span>\u00a0for this type of problem.<\/p>\nThe following chart shows how errors decrease with the iterations during training.<\/p>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/Quasi-Newton_s11_db.png\")
<\/p>\n
As the previous figure shows, the curves have converged.<\/p>\n\n\n\n\n\n\n\n
This dataset was generated using HFSS software, with the radiation frequency set at 2.4 GHz, a frequency commonly used for Bluetooth and WLAN operations, which can be utilized to optimize the design and performance of patch antennas.<\/p>\n
1. Application type<\/h2>\n<\/section>\n
The predicted variable in this application is the coefficient of reflection, S11, for a patch antenna.<\/p>\n
Therefore, this is an approximation project.<\/p>\n
Optimizing the antenna design aims to achieve the lowest possible value for S11, signifying high power transmission and minimal reflection levels, employing artificial intelligence and machine learning.<\/p>\n This dataset features information on patch antennas, a type of microstrip antenna widely used in wireless communications.<\/p>\n The dataset includes various dimensions and parameters of the antenna, including the operating frequency, dimensions of the patch and slots, and a measure of the antenna’s reflection coefficient. The data is organized into 8 clusters.<\/p>\n The number of input variables<\/a>, or attributes for each sample, is 7. The target variable<\/a> is S11.<\/p>\n The following list summarizes the variables’<\/a> information:<\/p>\n<\/section>\n Each instance<\/a>\u00a0contains the input and target variables of a different patient.<\/p>\n The data set is divided into training, validation, and testing subsets.<\/p>\n Neural Designer automatically assigns 60% of the instances for training, 20% for selection, and 20% for testing.<\/p>\n The\u00a0input-target correlations<\/a> might indicate which factors have the most significant influence on the reflection coefficient<\/span>. The next step is to set\u00a0up a\u00a0neural network<\/a> that represents<\/span> the approximation function.<\/p>\n For this class of applications, the neural network consists of the following components:<\/p>\n The scaling layer<\/a> contains the statistics on the inputs calculated from the data file and the method for scaling the input variables.<\/p>\n Here, the minimum-maximum method<\/a> has been set. As we use 7 input variables, the scaling layer has 7 inputs.<\/p>\n We use 2 dense layers here.<\/p>\n The first dense layer has 7 inputs, 3 neurons, and a hyperbolic tangent activation function<\/a><\/p>\n The second dense layer has 3 inputs, 1 neuron, and a linear activation function<\/a><\/p>\n The unscaling layer<\/a> contains the statistics of the output.<\/p>\n The following figure is a graphical representation of this neural network. The fourth step is to set the training strategy<\/a>, which is composed of two terms:<\/p>\n The loss index<\/a> is the weighted squared error<\/a> with L2 regularization<\/a>, the default loss index for binary classification applications.<\/p>\n We can state the learning problem as finding a neural network that minimizes the loss index.<\/p>\n That is a neural network that fits the data set (error term<\/a>) and does not oscillate (regularization term<\/a>).<\/p>\n The optimization algorithm<\/a>\u00a0we use is the\u00a0quasi-Newton method<\/a>, which is also the standard approach<\/span>\u00a0for this type of problem.<\/p>\n The following chart shows how errors decrease with the iterations during training.<\/p>\n As the previous figure shows, the curves have converged.<\/p>\n2. Data set<\/h2>\n
Variables<\/h3>\n
Antenna Dimensions<\/strong><\/h4>\n
\n
Slot Dimensions<\/strong><\/h4>\n
\n
Operating Parameters<\/strong><\/h4>\n
\n
Instances<\/h3>\n
Correlations<\/h3>\n
\n
\nHere, the most correlated variables with survival status are area_slot_mm2<\/b> and slot_length_mm<\/b>.<\/p>\n<\/section>\n3. Neural network<\/h2>\n
\n
Scaling layer<\/h3>\n
Dense layers<\/h3>\n
Unscaling layer<\/h3>\n
\n<\/p>\n<\/section>\n4. Training strategy<\/h2>\n
\n
Loss index<\/h3>\n
Optimization algorithm<\/h3>\n
<\/p>\n