{"id":3407,"date":"2025-11-25T10:59:21","date_gmt":"2025-11-25T09:59:21","guid":{"rendered":"https:\/\/neuraldesigner.com\/blog\/modelling-process\/"},"modified":"2025-11-27T14:54:18","modified_gmt":"2025-11-27T13:54:18","slug":"modelling-process","status":"publish","type":"blog","link":"https:\/\/www.neuraldesigner.com\/blog\/modelling-process\/","title":{"rendered":"The modelling process with neural networks"},"content":{"rendered":"\t\t
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Mathematically, we can formulate the modeling process with neural networks from a variational perspective.\u00a0<\/span><\/p>

Neural networks are the most crucial technique for machine learning and artificial intelligence.\u00a0\u00a0<\/p>

Indeed, building a model consists of finding a function that causes a loss functional to assume an extreme value.<\/p>

The following figure illustrates a class diagram that represents the concepts involved in the modeling process.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

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Contents<\/h2>\t\t\t\t<\/div>\n\t\t
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\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t1.Dataset<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t2.Neural network<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t3.Training strategy<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t4.Model selection<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t5.Testing analysis<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\t6.Model deployment<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Next, we introduce these six concepts.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

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1. Dataset<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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The data set contains information for creating our model.\u00a0<\/p>

The information may include numerical measurements, text, images, and other relevant content.\u00a0<\/p>

It is a data collection structured in a table format, consisting of rows and columns.<\/p>

A dataset comprises a matrix and information about the columns or variables, as well as the rows or samples.\u00a0<\/p>

Variables can be used as\u00a0inputs<\/i>,\u00a0targets, or\u00a0<\/i>unused<\/i>.\u00a0<\/p>

Samples can be used for training<\/i>, selection<\/i>, testing<\/i>, or unused<\/i>.<\/p>

The following is an example of a data set in the automotive sector.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

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Example: Electric motor data set<\/h3>\t\t\t\t<\/div>\n\t\t\t\t
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An automotive company aims to develop a digital twin of an electric motor utilizing artificial intelligence.\u00a0<\/p>

Having robust rotor and stator temperature estimators helps the automotive industry improve the motor’s efficiency by reducing power losses and, ultimately, heat buildup.<\/p>

The company uses the dataset to build the model.\u00a0<\/p>

The dataset comprises various sensor data collected from a permanent magnet synchronous motor (PMSM) deployed on a test bench.\u00a0<\/p>

The LEA department of the University of Paderborn collected the testbed measurements.\u00a0<\/p>

This data set consists of 107 samples.<\/p>

The following table illustrates the data set.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t

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ambient temperature<\/th>coolant temperature<\/th>voltage_d<\/th>voltage_q<\/th>…<\/th>stator_winding<\/th><\/tr>
-0.274<\/td>-1.070<\/td>0.180<\/td>1.681<\/td>…<\/th>-0.331<\/td><\/tr>
-0.274<\/td>-1.070<\/td>-1.243<\/td>0.483<\/td>…<\/th>0.712<\/td><\/tr>
-0.274<\/td>-1.070<\/td>-1.560<\/td>-0.504<\/td>…<\/th>1.519<\/td><\/tr>
-0.274<\/td>-1.070<\/td>0.298<\/td>0.958<\/td>…<\/th>-1.767<\/td><\/tr>
-0.274<\/td>-1.070<\/td>-0.963<\/td>0.642<\/td>…<\/th>-0.846<\/td><\/tr>
-0.274<\/td>-1.070<\/td>-1.498<\/td>-0.140<\/td>…<\/th>-0.947<\/td><\/tr>
-0.274<\/td>-1.070<\/td>-1.026<\/td>0.926<\/td>…<\/th>-0.346<\/td><\/tr>
…<\/td>…<\/td>…<\/td>…<\/td>…<\/td>…<\/td><\/tr>
-0.127<\/td>1.930<\/td>0.300<\/td>-1.292<\/td>…<\/th>0.372<\/td><\/tr><\/tbody><\/table><\/div>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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In this dataset, all variables are numeric.\u00a0<\/p>

The input variables are ambient_temperature, coolant_temperature, voltage_d, voltage_q, voltage_module, current_d, current_q and current_module.<\/p>

The target variables are motor_speed, torque, stator_yoke and stator_tooth, stator_winding.<\/p>

The samples are divided into 60% training samples (65), 20% selection samples (21), and the remaining 20% testing samples (21).<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t

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2. Neural network<\/h2>\t\t\t\t<\/div>\n\t\t\t\t
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An artificial neural network, or simply a neural network, can be defined as a biologically inspired computational algorithm consisting of a network architecture composed of artificial neurons.<\/p>

This structure contains a set of parameters tuned to perform specific tasks.\u00a0<\/p>

The neural network represents the model.<\/p>

Neural networks are organized in layers.<\/p>