The instances<\/a> are randomly split into 60% training, 20% validation, and 20% testing.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n Calculating the data distributions<\/a> helps us verify the accuracy of the available information and detect anomalies.<\/p>\n It is also interesting to look for dependencies between a single input and a single target variable.<\/p>\n To do that, we can plot an\u00a0input-target correlations<\/a> chart.<\/p>\n In this case, the highest correlation is with the distance to solar noon (the solar plant generates the closer to solar noon, the more power).<\/p>\n Next, we plot a scatter chart<\/a> for the most significant correlations for our target variable.<\/p>\n The second step is to build a neural network that represents the approximation function. Approximation models usually contain the following layers:<\/p>\n The neural network has nine inputs (distance to solar noon, temperature, wind direction, wind speed, sky cover, visibility, humidity, average wind speed (period), and average pressure (period)) and one output (power generated).<\/p>\n The scaling layer<\/a> contains the statistics of the inputs. We use the automatic setting for this layer to accommodate the best scaling technique for our data.<\/p>\n We use 2 perceptron layers here.<\/p>\n The hidden perceptron layer has 9 inputs, 3 neurons, and a hyperbolic tangent activation function<\/a>.<\/p>\n The output perceptron layer has 3 inputs, 1 neuron, and a linear activation function<\/a>.<\/p>\n The unscaling layer<\/a> contains the statistics of the outputs. We use the automatic method as before.<\/p>\n The following graph represents the neural network for this example.<\/p>\n The fourth step is to select an appropriate training strategy<\/a>.<\/p>\n It is composed of two concepts:<\/p>\n The loss index<\/a> defines what the neural network will learn. It is composed of an error term<\/a> and a regularization term<\/a>.<\/p>\n The error term we choose is the normalized squared error<\/a>. It divides the squared error between the neural network outputs and the data set’s targets by its normalization coefficient. If the normalized squared error is 1, the neural network predicts the data ‘in the mean’, while a value of 0 means a perfect data prediction. This error term has no parameters to set.<\/p>\n The regularization term is the L2 regularization<\/a>. It controls the neural network’s complexity by reducing the values of the parameters. We use a weak weight for this regularization term.<\/p>\n The optimization algorithm<\/a> is responsible for searching for the neural network parameters that minimize the loss index.<\/p>\n Here, we chose the quasi-Newton method<\/a> as an optimization algorithm.<\/p>\n The following chart shows how the training error (blue) and the selection error (orange) decrease with the number of epochs during training.<\/p>\n The final values are training error = 0.121 NSE<\/b> and selection error = 0.122 NSE<\/b>, respectively.<\/p>\n<\/section>\n The objective of model selection<\/a> is to find the network architecture with the best generalization properties.<\/p>\n We aim to reduce the final selection error obtained previously (0.122 NSE).<\/p>\n The best selection error is achieved using a model with the most appropriate complexity to produce a good data fit.<\/p>\n Order selection<\/a> algorithms are responsible for finding the optimal number of perceptrons in the neural network.<\/p>\n The following chart shows the results of the incremental order<\/a> algorithm.<\/p>\n The blue line shows training error and the orange line shows selection error, both versus the number of neurons.<\/p>\n As we can see, the final training error continuously decreases with the number of neurons. However, the final selection error takes a minimum value at some point.<\/p>\n The optimal number of neurons is 8, corresponding to a selection error of 0.089 NSE<\/b>.<\/p>\n The following figure shows the optimal network architecture for this application.<\/p>\n The purpose of the testing analysis<\/a> is to validate the generalization capabilities of the neural network.<\/p>\n We use the testing instances<\/a> in the data set, which have never been used before.<\/p>\n A standard testing method in approximation applications is to perform a linear regression analysis<\/a> between the predicted and the real values.<\/p>\n For a perfect fit, the correlation coefficient R2 would be 1.\u00a0With\u00a0R2 = 0.951<\/strong>, the neural network accurately predicts the testing data<\/span>.<\/p>\n<\/section>\n In the model deployment<\/a> phase, the neural network predicts outputs for inputs it has not seen before.<\/p>\n We can calculate the neural network outputs<\/a> for a given set of inputs:<\/p>\n The predicted output for these input values is the following:<\/p>\n Directional outputs<\/a> plot the neural network outputs through some reference points.<\/p>\n The next list shows the reference point for the plots.<\/p>\n We can see here how the distance to solar noon affects the power generated:<\/p>\nDistributions<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/solar-gen-power-generated-distribution.webp\")
<\/p>\nInput-target correlations<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/solar-gen-correlations.webp\")
<\/p>\nScatter charts<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/solar-gen-power-generated-vs-distance-to-solar-noon.webp\")
<\/p>\n<\/section>\n3. Neural network<\/h3>\n
\n
Scaling layer<\/h3>\n
Desnse layers<\/h3>\n
Unscaling layer<\/h3>\n
Neural network graph<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/solar-gen-initial-neural-network.webp\")
<\/p>\n<\/section>\n4. Training strategy<\/h2>\n
\n
Loss index<\/h3>\n
Optimization algorithm<\/h3>\n
Training<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/solar-gen-training-history.webp\")
<\/p>\n5. Model selection<\/h2>\n
Neuron selection<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/solar-gen-order-selection.webp\")
<\/p>\nNeural network graph<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/solar-gen-final-architecture.webp\")
<\/p>\n<\/section>\n6. Testing analysis<\/h2>\n
Goodnes-of-fit<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/solar-gen-linear-regression-analysis.webp\")
<\/p>\n7. Model deployment<\/h2>\n
Neural network outputs<\/h3>\n
\n
\n
Directional outputs<\/h3>\n
\n
![](\"https:\/\/www.neuraldesigner.com\/images\/solar-gen-power-generated-distance-to-solar-noon-directional-output.webp\")
<\/p>\n8. Video tutorial<\/h2>\n<\/section>\n