{"id":165,"date":"2022-03-14T18:23:42","date_gmt":"2022-03-14T17:23:42","guid":{"rendered":"https:\/\/naupacte.com\/index.php\/navpactos-un-langage-pour-les-acteurs-de-la-simulation-english\/"},"modified":"2026-06-22T19:10:34","modified_gmt":"2026-06-22T17:10:34","slug":"numerical-modeling-simulation-actors-2","status":"publish","type":"page","link":"https:\/\/naupacte.com\/index.php\/en\/numerical-modeling-simulation-actors-2\/","title":{"rendered":"Native automatic differentiation for coupled non-linear multiphysics"},"content":{"rendered":"\n<p>Naupacte designed the expected language for the players in digital modeling and simulation. Linear and non-linear systems coming from <strong>multiphysics<\/strong> models are easily formulated and a brand new <strong>automatic differentiation<\/strong> is provided for <strong>optimisation<\/strong> process.<\/p>\n\n\n\n<p>Naupacte&nbsp;helps&nbsp;you&nbsp;formulate&nbsp;new&nbsp;multiphysics&nbsp;problems&nbsp;and optimize&nbsp;the associated&nbsp;designs,&nbsp;thanks&nbsp;to&nbsp;a&nbsp;new&nbsp;tensor&nbsp;formulation&nbsp;language and&nbsp;unique internal&nbsp;automatic&nbsp;differentiation&nbsp;capabilities,&nbsp;while&nbsp;ensuring&nbsp;outstanding assembly&nbsp;computation&nbsp;performance.<\/p>\n\n\n\n<p>Navpactos&nbsp;is&nbsp;a&nbsp;C++&nbsp;library&nbsp;implementing&nbsp;a&nbsp;language&nbsp;intended&nbsp;to&nbsp;formulate in formal&nbsp;algebra&nbsp;multiphysical&nbsp;applications&nbsp;(for&nbsp;example&nbsp;of&nbsp;finite&nbsp;element type)&nbsp;with&nbsp;automatic&nbsp;differentiation&nbsp;internally&nbsp;in&nbsp;support&nbsp;of&nbsp;the&nbsp;optimal design algorithms;&nbsp;second&nbsp;order&nbsp;methods&nbsp;become&nbsp;possible&nbsp;on&nbsp;the&nbsp;optimality equations,&nbsp;and&nbsp;this,&nbsp;entirely&nbsp;automatically.<\/p>\n\n\n\n<p>Concretely, during execution, Navpactos performs <strong>the automatic differentiation of your digital models of coupled multiphysics based on finite elements<\/strong>, to not only provide the gradient or the adjoint (first-order derivative) but also the jacobian of the gradient (second order derivative, thus including the differentiation of the tangent matrix of the state equation).<\/p>\n\n\n\n<p>This&nbsp;is&nbsp;the&nbsp;result&nbsp;of&nbsp;20&nbsp;years&nbsp;of&nbsp;development&nbsp;led&nbsp;by&nbsp;a&nbsp;specialist&nbsp;in numerical simulation&nbsp;software.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Numerical simulation players<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Simulation Software Publishers<\/strong>: retain control of valuable skills.<\/li>\n\n\n\n<li><strong>Mathematicians &#8211; Research Centers &#8211; Developers<\/strong>: Unprecedented ease, performance and functionality to drive innovation.<\/li>\n\n\n\n<li><strong>Mathematical programming environments<\/strong>: Propose a finite element calculation module.<\/li>\n\n\n\n<li><strong>Engineering and Simulation Design Offices<\/strong>: Integrate custom solutions into your application portfolio.<\/li>\n\n\n\n<li><strong>Pre-trained simulation models providers<\/strong>: multiphysics foundation models, including sensitivity towards the parameters.<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/naupacte.com\/index.php\/en\/numerical-simulation-actors-detailed-2\">more on the benefits<\/a><\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Highlights of Navpactos language<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Integrability<\/strong>:&nbsp;as&nbsp;a&nbsp;C++&nbsp;library.<\/li>\n\n\n\n<li><strong>Power&nbsp;and&nbsp;functionality<\/strong>:&nbsp;the language&nbsp;is&nbsp;familiar&nbsp;with&nbsp;finite&nbsp;elements,&nbsp;sparse&nbsp;matrices,&nbsp;functions&nbsp;and&nbsp;fields;&nbsp;uses <strong>tensorial <\/strong><strong>computer algebra system<\/strong>,&nbsp;offers&nbsp;<strong>automatic&nbsp;differentiation<\/strong>.<\/li>\n\n\n\n<li><strong>Rapid&nbsp;development&nbsp;and&nbsp;readability&nbsp;of&nbsp;the&nbsp;code<\/strong>:&nbsp;the&nbsp;designer&nbsp;develops&nbsp;his&nbsp;methods&nbsp;without&nbsp;programming&nbsp;the calculations,&nbsp;just&nbsp;by&nbsp;formulating&nbsp;them.<\/li>\n\n\n\n<li><strong>Reduced&nbsp;maintenance&nbsp;and&nbsp;portability<\/strong>:&nbsp;performing&nbsp;calculations&nbsp;is&nbsp;supported&nbsp;by&nbsp;the&nbsp;library.<\/li>\n\n\n\n<li><strong>Code&nbsp;reliability<\/strong>:&nbsp;the formal&nbsp;representation&nbsp;allows&nbsp;checks&nbsp;before&nbsp;calculations&nbsp;are&nbsp;performed.<\/li>\n\n\n\n<li><strong>Speed&nbsp;of&nbsp;execution<\/strong>:&nbsp;Naupacte&#8217;s&nbsp;expertise and formal&nbsp;representation&nbsp;combine&nbsp;to&nbsp;deliver&nbsp;outstanding&nbsp;performance.<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-right is-layout-flex wp-container-core-buttons-is-layout-765c4724 wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-outline is-style-outline--1\"><a class=\"wp-block-button__link has-light-gray-background-color has-background wp-element-button\" href=\"https:\/\/naupacte.com\/index.php\/en\/tensor-algebra-embedded-language-for-numerical-simulation-2\">&#8230; on NAVPACTOS language<\/a><\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Towards optimal design<\/h2>\n\n\n\n<p><strong>Numerical simulation<\/strong> provides insight for the physical behavior of objects. The more frequently, it is just one phase of an <strong>optimisation<\/strong> workflow where the design of the object is driven towards more performance.<\/p>\n\n\n\n<p>Navpactos provides a great and expected functionality with its internal <strong>automatic differentiation<\/strong> that can be used to fill optimisation algorithms with <strong>gradients<\/strong> or <strong>sensitivities<\/strong> in order to accelerate the process. Would you consider the automatic derivation of optimality equations and their linearization?<\/p>\n\n\n\n<div class=\"wp-block-buttons is-content-justification-right is-layout-flex wp-container-core-buttons-is-layout-765c4724 wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button is-style-outline is-style-outline--2\"><a class=\"wp-block-button__link has-light-gray-background-color has-background wp-element-button\" href=\"https:\/\/naupacte.com\/index.php\/en\/tensor-algebra-embedded-language-for-numerical-simulation-2\/automatic-differentiation-and-computing\/\">&#8230; on automatic differentiation in navpactos<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Naupacte designed the expected language for the players in digital modeling and simulation. Linear and non-linear systems coming from multiphysics models are easily formulated and a brand new automatic differentiation is provided for optimisation process. Naupacte&nbsp;helps&nbsp;you&nbsp;formulate&nbsp;new&nbsp;multiphysics&nbsp;problems&nbsp;and optimize&nbsp;the associated&nbsp;designs,&nbsp;thanks&nbsp;to&nbsp;a&nbsp;new&nbsp;tensor&nbsp;formulation&nbsp;language and&nbsp;unique internal&nbsp;automatic&nbsp;differentiation&nbsp;capabilities,&nbsp;while&nbsp;ensuring&nbsp;outstanding assembly&nbsp;computation&nbsp;performance. Navpactos&nbsp;is&nbsp;a&nbsp;C++&nbsp;library&nbsp;implementing&nbsp;a&nbsp;language&nbsp;intended&nbsp;to&nbsp;formulate in formal&nbsp;algebra&nbsp;multiphysical&nbsp;applications&nbsp;(for&nbsp;example&nbsp;of&nbsp;finite&nbsp;element type)&nbsp;with&nbsp;automatic&nbsp;differentiation&nbsp;internally&nbsp;in&nbsp;support&nbsp;of&nbsp;the&nbsp;optimal design algorithms;&nbsp;second&nbsp;order&nbsp;methods&nbsp;become&nbsp;possible&nbsp;on&nbsp;the&nbsp;optimality equations,&nbsp;and&nbsp;this,&nbsp;entirely&nbsp;automatically. Concretely, during execution, Navpactos performs the automatic differentiation of your digital models of coupled multiphysics based on finite elements, to not only provide the gradient or the adjoint (first-order derivative) but also the jacobian of the gradient (second order derivative, thus including the differentiation of the tangent matrix of the state equation). This&nbsp;is&nbsp;the&nbsp;result&nbsp;of&nbsp;20&nbsp;years&nbsp;of&nbsp;development&nbsp;led&nbsp;by&nbsp;a&nbsp;specialist&nbsp;in numerical simulation&nbsp;software. Numerical simulation players Highlights of Navpactos language Towards optimal design Numerical simulation provides insight for the physical behavior of objects. The more frequently, it is just one phase of an optimisation workflow where the design of the object is driven towards more performance. Navpactos provides a great and expected functionality with its internal automatic differentiation that can be used to fill optimisation algorithms with gradients or sensitivities in order to accelerate the process. Would you consider the automatic derivation of optimality equations and their linearization?<\/p>\n","protected":false},"author":1,"featured_media":86,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-165","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/naupacte.com\/index.php\/wp-json\/wp\/v2\/pages\/165","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/naupacte.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/naupacte.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/naupacte.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/naupacte.com\/index.php\/wp-json\/wp\/v2\/comments?post=165"}],"version-history":[{"count":31,"href":"https:\/\/naupacte.com\/index.php\/wp-json\/wp\/v2\/pages\/165\/revisions"}],"predecessor-version":[{"id":718,"href":"https:\/\/naupacte.com\/index.php\/wp-json\/wp\/v2\/pages\/165\/revisions\/718"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/naupacte.com\/index.php\/wp-json\/wp\/v2\/media\/86"}],"wp:attachment":[{"href":"https:\/\/naupacte.com\/index.php\/wp-json\/wp\/v2\/media?parent=165"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}