{"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":"2026-08-26T13:48:26","modified_gmt":"2026-08-26T11:48:26","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>The model of a process is a mathematical description that adequately predicts the physical system&#8217;s response to all anticipated inputs.<\/p>\n<p>More specifically, it relates the performance variables with the state and control 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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