{"id":22515,"date":"2026-07-16T13:30:12","date_gmt":"2026-07-16T11:30:12","guid":{"rendered":"https:\/\/www.neuraldesigner.com\/use-cases\/performance-optimization\/"},"modified":"2026-10-12T13:35:19","modified_gmt":"2026-10-12T11:35:19","slug":"performance-optimization","status":"publish","type":"page","link":"https:\/\/www.neuraldesigner.com\/use-cases\/performance-optimization\/","title":{"rendered":"Performance optimization using machine learning"},"content":{"rendered":"<style>\n.nd-math-block {\n  display: block;\n  max-width: 100%;\n  overflow-x: auto;\n  margin: 1rem 0;\n  padding: 0.45rem 0;\n  text-align: center;\n}\n.nd-math-block math {\n  font-size: 1.04em;\n}\n<\/style>\n<style>.ndb{width:100vw;margin-left:calc(50% - 50vw);background:#eeeeee;padding:22px 24px 14px;font-family:\"Outfit\",\"Roboto\",Arial,sans-serif;color:#1b2635}.ndb *{box-sizing:border-box}.ndb a{text-decoration:none}.ndb-wrap{width:min(100%,960px);margin:0 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6px!important;color:#2d799f!important;box-shadow:none!important;border-radius:0!important}.ndb-card p:has(>img),.ndb-card figure,.ndb-lead p:has(>img),.ndb-lead figure{max-width:560px!important;margin-left:auto!important;margin-right:auto!important;text-align:center!important}.ndb-card p:has(>.nd-usecase-icon-source),.ndb-card .nd-usecase-icon-source{max-width:none!important}.ndb-card table:has(td h3){background:transparent!important;box-shadow:none!important;border:0!important;width:100%!important;table-layout:fixed!important;margin:14px 0!important}.ndb-card table:has(td h3) td{background:transparent!important;border:0!important;text-align:center!important;vertical-align:top!important;padding:16px 14px!important}.ndb-card table:has(td h3) td p{margin:0 0 12px!important;text-align:center!important;max-width:none!important}.ndb-card table:has(td h3) td p img{display:inline-block!important;width:52px!important;height:52px!important;max-width:52px!important;object-fit:contain!important;margin:0 auto!important;box-shadow:none!important;border-radius:0!important}.ndb-card table:has(td h3) td h3{color:#001233!important;font-size:16px!important;font-weight:600!important;margin:0!important;text-align:center!important;letter-spacing:.03em}body.page-child.parent-pageid-22498 main.site-main .ndb-wrap .ndb-card table td p img{width:52px!important;height:52px!important;max-width:52px!important;min-width:0!important;object-fit:contain!important;margin:0 auto!important;display:inline-block!important}main#content .ndb-card .nd-usecase-title-icon,main#content .ndb-card h3.nd-usecase-icon-title img{display:none!important}main#content .ndb-card h3.nd-usecase-icon-title{display:block!important}.ndb-card .ndb-subhead{color:#001233!important;font-size:19px!important;font-weight:600!important;margin:26px 0 8px!important;text-align:center!important}.ndb-card table:has(td h3) td p:not(:has(img)){font-size:14px!important;line-height:1.5!important;color:#51606f!important;margin:8px auto 0!important;text-align:center!important;max-width:none!important}<\/style><div class=\"ndb\"><div class=\"ndb-wrap\"><div class=\"ndb-lead\"><p>Tracking the behavior of a system allows us to predict its behavior and improve its performance.<\/p>\n<p>However, the performance of a process may depend on a large number of variables. Therefore, sophisticated methods and tools are needed to untangle all these factors effectively.<\/p>\n<p>This article explains how to use machine learning and <a href=\"https:\/\/www.neuraldesigner.com\/\">Neural Designer<\/a>\u00a0to model engineering systems and optimize industrial processes.<\/p>\n<h3>Contents<\/h3>\n<ol>\n<li><a href=\"#DataSet\">Data set<\/a>.<\/li>\n<li><a href=\"#MathematicalModel\">Mathematical model<\/a>.<\/li>\n<li><a href=\"#ResponseOptimization\">Response optimization<\/a>.<\/li>\n<li><a href=\"#Conclusions\">Conclusions<\/a>.<\/li>\n<\/ol>\n<\/div><ul class=\"ndb-toc\"><li><a href=\"#data-set\">Data set<\/a><\/li><li><a href=\"#mathematical-model\">Mathematical model<\/a><\/li><li><a href=\"#response-optimization\">Response optimization<\/a><\/li><li><a href=\"#conclusions\">Conclusions<\/a><\/li><\/ul><div class=\"ndb-card\" id=\"data-set\"><h2>Data set<\/h2><p>The <a href=\"https:\/\/www.neuraldesigner.com\/learning\/tutorials\/data-set\/\">data set<\/a> contains measurements from our system or process.<\/p>\n<p>It comprises state, control, and performance <a href=\"https:\/\/www.neuraldesigner.com\/learning\/tutorials\/data-set\/#Variables\">variables<\/a>.<\/p>\n<p><b>State variables<\/b> are those <a href=\"https:\/\/www.neuraldesigner.com\/learning\/tutorials\/data-set\/#InputVariables\">inputs<\/a>\u00a0that determine the system&#8217;s performance and are not actionable by the company&#8217;s technicians.<\/p>\n<p>Some examples of state variables are:<\/p>\n<ul>\n<li>The ambient temperature in a combined cycle power plant.<\/li>\n<li>The water salinity in a desalination plant.<\/li>\n<\/ul>\n<p><b>\u00a0<\/b><\/p>\n<p><b>Control variables<\/b> are those\u00a0<a href=\"https:\/\/www.neuraldesigner.com\/learning\/tutorials\/data-set\/#InputVariables\">inputs<\/a> that determine the system&#8217;s performance and can be set by the company&#8217;s technicians.<\/p>\n<p>Two examples of the control variables are:<\/p>\n<ul>\n<li>The velocity of an aircraft.<\/li>\n<li>The combustion airflow in a furnace.<\/li>\n<\/ul>\n<p><b>\u00a0<\/b><\/p>\n<p><b>Performance variables<\/b> are the system&#8217;s <a href=\"https:\/\/www.neuraldesigner.com\/learning\/tutorials\/data-set\/#TargetVariables\">outputs<\/a>\u00a0and depend on the state and the control variables.<\/p>\n<p>Performance optimization can consider different targets:<\/p>\n<p><img decoding=\"async\" style=\"width: 50px;\" src=\"https:\/\/www.neuraldesigner.com\/images\/efficiency.svg\" \/><\/p>\n<h3>PROCESS EFFICIENCY<\/h3>\n<p><img decoding=\"async\" style=\"width: 50px;\" src=\"https:\/\/www.neuraldesigner.com\/images\/consumption.svg\" \/><\/p>\n<h3>ENERGY CONSUMPTION<\/h3>\n<p><img decoding=\"async\" style=\"width: 50px;\" src=\"https:\/\/www.neuraldesigner.com\/images\/pollution.svg\" \/><\/p>\n<h3>GAS EMISSIONS<\/h3>\n<p><img decoding=\"async\" style=\"width: 50px;\" src=\"https:\/\/www.neuraldesigner.com\/images\/noise.svg\" \/><\/p>\n<h3>NOISE LEVELS<\/h3>\n<\/div><div class=\"ndb-card\" id=\"mathematical-model\"><h2>Mathematical model<\/h2><p>A mathematical model of the process predicts the performance of the system, such as its efficiency or its energy consumption, under given operating conditions. To be useful for optimization, its predictions must stay reliable over the whole range of conditions that the optimizer may explore.<\/p>\n<p>In other words, the model is a function that takes the state and control variables as inputs and returns the performance variables:<\/p>\n<p><span class=\"nd-math-block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mtext>performance_variables<\/mtext><mo>=<\/mo><mtext>function<\/mtext><mo stretchy=\"false\">(<\/mo><mtext>state_variables<\/mtext><mo>,<\/mo><mtext>control_variables<\/mtext><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">performance_variables = function(state_variables, control_variables)<\/annotation><\/semantics><\/math><\/span><\/p>\n<p><a href=\"https:\/\/www.neuraldesigner.com\/learning\/tutorials\/neural-network\/\">Neural networks<\/a> are algorithms that fit multi-dimensional and non-linear functions from data sets.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.neuraldesigner.com\/images\/performance-optimization-neural-network.webp\" \/><\/p>\n<p>The inputs to the neural network include the state and control variables. The outputs from the neural network are the predicted performance variables of the system for that scenario.<\/p>\n<\/div><div class=\"ndb-card\" id=\"response-optimization\"><h2>Response optimization<\/h2><p>The objective of the response optimization algorithm is to exploit the mathematical model to look for optimal operating conditions.<\/p>\n<p>Indeed, the predictive model allows us to simulate different operating scenarios and adjust the control variables to improve efficiency.<\/p>\n<p>More specifically, we can formulate a performance optimization task as follows:<\/p>\n<p style=\"border: 1px solid; text-align: center;\"><b>For a given set of states, determine the controls that minimize or maximize the performance variables.<br \/>\n<\/b><\/p>\n<p>The following figure illustrates the response optimization process.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.neuraldesigner.com\/images\/response-optimization.svg\" \/><\/p>\n<p>As we can see, for a given state value, <b>s<\/b>, the control value, <b>c*<\/b>, minimizes the performance value.<\/p>\n<p>A performance optimization problem might also include a set of constraints on the system&#8217;s inputs and outputs.<\/p>\n<p>An example is to minimize the fuel consumption of an aircraft while maintaining the speed at the desired value.<\/p>\n<\/div><div class=\"ndb-card ndb-card--accent\" id=\"conclusions\"><h2>Conclusions<\/h2><p>Machine learning is a powerful technique to predict the performance of engineering systems.<\/p>\n<p>That allows us to simulate different operating scenarios and adjust the control parameters to improve efficiency.<\/p>\n<p>Some examples of performance optimization are improving process efficiency or reducing energy consumption.<\/p>\n<p><a href=\"https:\/\/www.neuraldesigner.com\/downloads\/\">Neural Designer<\/a> uses neural networks to model the behavior of systems. It also contains response optimization algorithms to fine-tune the control variables and optimize performance.<\/p>\n<\/div><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p>Tracking the behavior of a system allows us to predict its behavior and improve its performance. However, the performance of a process may depend on a large number of variables. Therefore, sophisticated methods and tools are needed to untangle all these factors effectively. 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