{"id":3532,"date":"2025-11-25T11:12:58","date_gmt":"2025-11-25T10:12:58","guid":{"rendered":"https:\/\/neuraldesigner.com\/learning\/model-deployment\/"},"modified":"2025-11-27T12:55:45","modified_gmt":"2025-11-27T11:55:45","slug":"model-deployment","status":"publish","type":"learning","link":"https:\/\/www.neuraldesigner.com\/learning\/tutorials\/model-deployment\/","title":{"rendered":"Machine learning tutorial: Model deployment"},"content":{"rendered":"<p>Deployment in machine learning is the process of applying a model to make predictions on new data.<\/p>\n<p>It involves organizing and presenting the learned knowledge so that it can be used effectively by the customer.<\/p>\n<p>Depending on the needs, deployment can be as simple as producing a report or as advanced as setting up a continuous learning system.<\/p>\n<p>You can use the following techniques for deploying a neural network:<\/p>\n<ul>\n<li><b><a href=\"#NeuralNetworkOutputs\">7.1. Neural network outputs<\/a><\/b><\/li>\n<li><b><a href=\"#OutputData\">7.2. Output data<\/a><\/b><\/li>\n<li><b><a href=\"#DirectionalOutputs\">7.3. Directional outputs<\/a><\/b><\/li>\n<li><b><a href=\"#MathematicalExpression\">7.4. Mathematical expression<\/a><\/b><\/li>\n<li><b><a href=\"#PythonExpression\">7.5. Python expression<\/a><\/b><\/li>\n<li><b><a href=\"#CExpression\">7.6. C++ expression<\/a><\/b><\/li>\n<\/ul>\n<section>\n<h2 id=\"NeuralNetworkOutputs\">7.1. Neural network outputs<\/h2>\n<p>A neural network produces a set of outputs for each set of inputs applied.<\/p>\n<p>The table below shows input attributes and their corresponding outputs when estimating a car\u2019s fuel consumption.<\/p>\n<table>\n<tbody>\n<tr>\n<th>Cylinders<\/th>\n<th>Displacement<\/th>\n<th>Horsepower<\/th>\n<th>Weight<\/th>\n<th>Acceleration<\/th>\n<th>Model year<\/th>\n<th>Fuel consumption<\/th>\n<\/tr>\n<tr>\n<td>8<\/td>\n<td>307<\/td>\n<td>130<\/td>\n<td>3504<\/td>\n<td>12<\/td>\n<td>1980<\/td>\n<td>17 mpg<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<section>\n<h2 id=\"OutputData\">7.2. Output data<\/h2>\n<\/section>\n<p>Often, the goal is to predict outputs for multiple cases stored in a data file, where each row contains the input values.<\/p>\n<p>The model then produces a new file with the corresponding outputs.<\/p>\n<p>The table below shows how a neural network estimates conversion probabilities for customers in a marketing campaign based on engagement factors.<\/p>\n<section>\n<table>\n<tbody>\n<tr>\n<th>Recency<\/th>\n<th>Frequency<\/th>\n<th>Monetary<\/th>\n<th>Conversion<\/th>\n<\/tr>\n<tr>\n<td>2 months<\/td>\n<td>5 times<\/td>\n<td>125 USD<\/td>\n<td>70%<\/td>\n<\/tr>\n<tr>\n<td>5 months<\/td>\n<td>2 times<\/td>\n<td>20 USD<\/td>\n<td>8%<\/td>\n<\/tr>\n<tr>\n<td>3 months<\/td>\n<td>9 times<\/td>\n<td>225 USD<\/td>\n<td>85%<\/td>\n<\/tr>\n<tr>\n<td>4 months<\/td>\n<td>1 time<\/td>\n<td>15 USD<\/td>\n<td>5%<\/td>\n<\/tr>\n<tr>\n<td>1 months<\/td>\n<td>3 times<\/td>\n<td>70 USD<\/td>\n<td>75%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/section>\n<section>\n<h2 id=\"DirectionalOutputs\">7.3. Directional outputs<\/h2>\n<\/section>\n<p>By varying one input while keeping the others fixed, we can see how that factor influences the model\u2019s output.<\/p>\n<p>These <em data-start=\"119\" data-end=\"140\">directional outputs<\/em> are helpful not only for understanding the model but also for improving designs or processes.<\/p>\n<p>The following table shows the reference point for plotting all the directional output charts. In this case, the model <a href=\"https:\/\/www.neuraldesigner.com\/learning\/examples\/yacht-hydrodynamics-modeling\">estimates the residuary resistance of a sailing yacht as a function of design parameters and sailing conditions<\/a>.<\/p>\n<section>\n<table>\n<tbody>\n<tr>\n<td>Center of buoyancy<\/td>\n<td style=\"text-align: right;\">-2.38<\/td>\n<\/tr>\n<tr>\n<td>Prismatic coefficient<\/td>\n<td style=\"text-align: right;\">0.56<\/td>\n<\/tr>\n<tr>\n<td>length displacement<\/td>\n<td style=\"text-align: right;\">4.79<\/td>\n<\/tr>\n<tr>\n<td>Beam draught ratio<\/td>\n<td style=\"text-align: right;\">3.94<\/td>\n<\/tr>\n<tr>\n<td>length beam ratio<\/td>\n<td style=\"text-align: right;\">3.21<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>The following chart shows how the residuary resistance varies with the Froude number (which represents the velocity of the yacht), with all the other inputs being fixed.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.neuraldesigner.com\/images\/directional_output_example.webp\" \/><\/p>\n<p>As we can see, the residuary resistance increases exponentially for high values of the Froude number. Therefore, this yacht design does not perform well at high speeds.<\/p>\n<\/section>\n<section>\n<h2 id=\"MathematicalExpression\">7.4. Mathematical expression<\/h2>\n<div class=\"text-base my-auto mx-auto pb-10 [--thread-content-margin:--spacing(4)] thread-sm:[--thread-content-margin:--spacing(6)] thread-lg:[--thread-content-margin:--spacing(16)] px-(--thread-content-margin)\">\n<div class=\"[--thread-content-max-width:40rem] thread-sm:[--thread-content-max-width:40rem] thread-lg:[--thread-content-max-width:48rem] mx-auto max-w-(--thread-content-max-width) flex-1 group\/turn-messages focus-visible:outline-hidden relative flex w-full min-w-0 flex-col agent-turn\" tabindex=\"-1\">\n<div class=\"flex max-w-full flex-col grow\">\n<div class=\"min-h-8 text-message relative flex w-full flex-col items-end gap-2 text-start break-words whitespace-normal [.text-message+&amp;]:mt-5\" dir=\"auto\" data-message-author-role=\"assistant\" data-message-id=\"c9ab1a18-65b1-46e4-817b-e57f756f275d\" data-message-model-slug=\"gpt-5\">\n<div class=\"flex w-full flex-col gap-1 empty:hidden first:pt-[3px]\">\n<div class=\"markdown prose dark:prose-invert w-full break-words light markdown-new-styling\">\n<p data-start=\"0\" data-end=\"189\" data-is-last-node=\"\" data-is-only-node=\"\">A neural network represents a function that maps inputs to outputs, defined by its parameters.<\/p>\n<p data-start=\"0\" data-end=\"189\" data-is-last-node=\"\" data-is-only-node=\"\">This mathematical expression can then be embedded into other software for use in production.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p>Next, we list an example of the mathematical model represented by a neural network.<\/p>\n<pre>scaled_shear_rate = 2*(shear_rate-50)\/(90-50)-1;\r\nscaled_particle_diameter = 2*(particle_diameter-0.72)\/(6.596-0.72)-1;\r\ny_1_1 = tanh(-1.06007+(scaled_shear_rate*0.448487)+(scaled_particle_diameter*-0.861393));\r\ny_1_2 = tanh(0.756922+(scaled_shear_rate*2.00716)+(scaled_particle_diameter*0.391539));\r\ny_1_3 = tanh(0.862072+(scaled_shear_rate*-0.726115)+(scaled_particle_diameter*-1.46053));\r\nscaled_particles_adhering = (-1.30536+(y_1_1*-1.0244)+(y_1_2*0.56055)+(y_1_3*-0.565459));\r\nparticles_adhering = (0.5*(scaled_particles_adhering+1.0)*(74.75-13.22)+13.22);\r\n<\/pre>\n<p>You can easily embed the above code into any application that uses the model.<\/p>\n<p>For that, you only need to adapt the mathematical expression to the syntax of your programming language.<\/p>\n<\/section>\n<section>\n<h2 id=\"PythonExpression\">7.5. Python expression<\/h2>\n<p>We can export the mathematical expression the model represents to different programming languages, such as Python.<\/p>\n<p>The following example is a neural network implemented in the Python programming language.<\/p>\n<pre>def expression(inputs) : \r\nif type(inputs) != list:\r\nprint('Argument must be a list')\r\nreturn\r\nif len(inputs) != 4:\r\nprint('Incorrect number of inputs')\r\nreturn\r\ntemperature=inputs[0]\r\nexhaustt_vacuum=inputs[1]\r\nambient_pressure=inputs[2]\r\nrelative_humidity=inputs[3]\r\nscaled_temperature = (temperature-19.6512)\/7.45247\r\nscaled_exhaustt_vacuum = 2*(exhaustt_vacuum-25.36)\/(81.56-25.36)-1\r\nscaled_ambient_pressure = (ambient_pressure-1013.26)\/5.93878\r\nscaled_relative_humidity = (relative_humidity-73.309)\/14.6003\r\n\t\ty_1_1 = tanh (-0.155062+ (scaled_temperature*0.203034)+ (scaled_exhaustt_vacuum*0.731056)+ (scaled_ambient_pressure*-0.191671)+ (scaled_relative_humidity*0.0158643))\r\n\t\ty_1_2 = tanh (-0.29098+ (scaled_temperature*-0.023069)+ (scaled_exhaustt_vacuum*-0.263476)+ (scaled_ambient_pressure*-0.231774)+ (scaled_relative_humidity*0.333626))\r\n\t\ty_1_3 = tanh (0.570558+ (scaled_temperature*0.573079)+ (scaled_exhaustt_vacuum*-0.0279703)+ (scaled_ambient_pressure*0.111165)+ (scaled_relative_humidity*0.00867248))\r\n\t\tscaled_energy_output =  (0.15981+ (y_1_1*-0.383639)+ (y_1_2*-0.126028)+ (y_1_3*-0.745885))\r\nenergy_output = (0.5*(scaled_energy_output+1.0)*(495.76-420.26)+420.26)\r\n\t\treturn energy_output \r\n<\/pre>\n<p>You can easily integrate this code into any Python application that uses the model.<\/p>\n<\/section>\n<section>\n<h2 id=\"CExpression\">7.6. C++ expression<\/h2>\n<p>C++ is one of the most widely used programming languages.<\/p>\n<p>The following code is an example of a neural network in the C programming language.<\/p>\n<pre>#include \r\nusing namespace std;\r\nvector scaling_layer(const vector&amp; inputs)\r\n{\r\nvector outputs(5);\r\noutputs[0] = inputs[0]*0.3025558293-1;\r\noutputs[1] = inputs[1]*0.3025558293-1;\r\noutputs[2] = inputs[2]*0.4306863844-0.1386272311;\r\noutputs[3] = inputs[3]*5.421008924e-20-1;\r\noutputs[4] = inputs[4]*5.421008924e-20+1;\r\nreturn outputs;\r\n}\r\nvector perceptron_layer_0(const vector&amp; inputs)\r\n{\r\nvector combinations(3);\r\ncombinations[0] = 0.02009 -0.880635*inputs[0] +0.815813*inputs[1] -0.106329*inputs[2] -0.117222*inputs[3] -0.210783*inputs[4];\r\ncombinations[1] = 0.0355442 -0.0121058*inputs[0] +0.0725463*inputs[1] +0.0671187*inputs[2] -0.0893239*inputs[3] +0.205473*inputs[4];\r\ncombinations[2] = -0.00834767 +0.0153575*inputs[0] -0.00712658*inputs[1] +0.0125823*inputs[2] -0.0126559*inputs[3] -0.0117719*inputs[4];\r\nvector activations(3);\r\nactivations[0] = tanh(combinations[0]);\r\nactivations[1] = tanh(combinations[1]);\r\nactivations[2] = tanh(combinations[2]);\r\nreturn activations;\r\n}\r\nvector perceptron_layer_1(const vector&amp; inputs)\r\n{\r\nvector combinations(1);\r\ncombinations[0] = -0.044036 +1.01136*inputs[0] -0.244702*inputs[1] +0.00911695*inputs[2];\r\nvector activations(1);\r\nactivations[0] = combinations[0];\r\nreturn activations;\r\n}\r\nvector unscaling_layer(const vector&amp; inputs)\r\n{\r\nvector outputs(1);\r\noutputs[0] = inputs[0]*0.7265999913+0.7265999913;\r\nreturn outputs;\r\n}\r\nvector bounding_layer(const vector&amp; inputs)\r\n{\r\nvector outputs(1);\r\noutputs[0] = inputs[0];\r\nreturn outputs;\r\n}\r\nvector neural_network(const vector&amp; inputs)\r\n{\r\nvector outputs;\r\noutputs = scaling_layer(inputs);\r\noutputs = perceptron_layer_0(outputs);\r\noutputs = perceptron_layer_1(outputs);\r\noutputs = unscaling_layer(outputs);\r\noutputs = bounding_layer(outputs);\r\nreturn outputs;\r\n}\r\nint main(){return 0;}\r\n<\/pre>\n<p>You can easily embed the above code into any C++ application that uses the model.<\/p>\n<\/section>\n<section><a href=\"https:\/\/www.neuraldesigner.com\/learning\/tutorials\/testing-analysis\">\u21d0 Testing Analysis<\/a><br \/>\n<a style=\"float: right;\" href=\"https:\/\/www.neuraldesigner.com\/learning\/tutorials\/neural-networks-bibliography\">Bibliography \u21d2<\/a><\/section>\n","protected":false},"author":122,"featured_media":2702,"template":"","categories":[30],"tags":[36],"class_list":["post-3532","learning","type-learning","status-publish","has-post-thumbnail","hentry","category-tutorials","tag-tutorials"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Machine learning tutorial: Model deployment<\/title>\n<meta name=\"description\" content=\"Learn 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