{"id":2128,"date":"2021-09-18T20:59:30","date_gmt":"2021-09-19T00:59:30","guid":{"rendered":"https:\/\/engineering.jhu.edu\/zaki\/?page_id=2128"},"modified":"2021-09-18T21:02:21","modified_gmt":"2021-09-19T01:02:21","slug":"machine-learning","status":"publish","type":"page","link":"https:\/\/engineering.jhu.edu\/zaki\/research\/machine-learning\/","title":{"rendered":"Machine learning"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-2131 size-full\" src=\"https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Schematics_EDNN_a.png\" alt=\"\" width=\"879\" height=\"449\" srcset=\"https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Schematics_EDNN_a.png 879w, https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Schematics_EDNN_a-300x153.png 300w, https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Schematics_EDNN_a-768x392.png 768w, https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Schematics_EDNN_a-624x319.png 624w\" sizes=\"auto, (max-width: 879px) 100vw, 879px\" \/><\/p>\n<p>Evolutional Deep Neural Networks (EDNN) are a powerful new approach to solving partial differential equations (PDE). The parameters of the network are trained to represent the initial state of the system only, and are subsequently updated dynamically, without any further training, to provide an accurate prediction of the evolution of the PDE system. \u00a0In this framework, the network parameters are updated dynamically, using the governing equations. As such, the predictions accurately satisfy the governing equations, and trajectories can be evolved for indefinitely long times, which is not feasible for other neural network approaches.<\/p>\n<p>EDNN was invented by our research group (Du &amp; Zaki, Phys. Review E 2021). \u00a0 Its versatility, accuracy and predictive capabilities have been demonstrated for a wide range of applications including the heat transfer, nonlinear advection, chaotic dynamics and turbulent flows.<\/p>\n<p>Current applications of EDNN include predictions of flows around bluff bodies, transition to turbulence, and viscoelastic flows. \u00a0And example is shown below where EDNN was used to solve the evolution of Kolmogorov flow, which starts from a laminar initial state and transition to chaotic dynamics.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-2150 alignnone\" src=\"https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Kflow_n4_U_80000-300x251.png\" alt=\"\" width=\"300\" height=\"251\" srcset=\"https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Kflow_n4_U_80000-300x251.png 300w, https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Kflow_n4_U_80000-768x642.png 768w, https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Kflow_n4_U_80000-624x522.png 624w, https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Kflow_n4_U_80000.png 902w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-2152 alignnone\" src=\"https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Kflow_n4_V_80000-300x251.png\" alt=\"\" width=\"300\" height=\"251\" srcset=\"https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Kflow_n4_V_80000-300x251.png 300w, https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Kflow_n4_V_80000-768x642.png 768w, https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Kflow_n4_V_80000-624x522.png 624w, https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Kflow_n4_V_80000.png 902w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Evolutional Deep Neural Networks (EDNN) are a powerful new approach to solving partial differential equations (PDE). The parameters of the network are trained to represent the initial state of the system only, and are subsequently updated dynamically, without any further training, to provide an accurate prediction of the evolution of the PDE system. \u00a0In this [&hellip;]<\/p>\n","protected":false},"author":127,"featured_media":0,"parent":30,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"class_list":["post-2128","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Machine learning - Flow Science and Engineering<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/engineering.jhu.edu\/zaki\/research\/machine-learning\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Machine learning - Flow Science and Engineering\" \/>\n<meta property=\"og:description\" content=\"Evolutional Deep Neural Networks (EDNN) are a powerful new approach to solving partial differential equations (PDE). The parameters of the network are trained to represent the initial state of the system only, and are subsequently updated dynamically, without any further training, to provide an accurate prediction of the evolution of the PDE system. \u00a0In this [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/engineering.jhu.edu\/zaki\/research\/machine-learning\/\" \/>\n<meta property=\"og:site_name\" content=\"Flow Science and Engineering\" \/>\n<meta property=\"article:modified_time\" content=\"2021-09-19T01:02:21+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/engineering.jhu.edu\/zaki\/wp-content\/uploads\/2021\/09\/Schematics_EDNN_a.png\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/research\\\/machine-learning\\\/\",\"url\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/research\\\/machine-learning\\\/\",\"name\":\"Machine learning - Flow Science and Engineering\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/research\\\/machine-learning\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/research\\\/machine-learning\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/wp-content\\\/uploads\\\/2021\\\/09\\\/Schematics_EDNN_a.png\",\"datePublished\":\"2021-09-19T00:59:30+00:00\",\"dateModified\":\"2021-09-19T01:02:21+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/research\\\/machine-learning\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/research\\\/machine-learning\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/research\\\/machine-learning\\\/#primaryimage\",\"url\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/wp-content\\\/uploads\\\/2021\\\/09\\\/Schematics_EDNN_a.png\",\"contentUrl\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/wp-content\\\/uploads\\\/2021\\\/09\\\/Schematics_EDNN_a.png\",\"width\":879,\"height\":449},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/research\\\/machine-learning\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Research\",\"item\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/research\\\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Machine learning\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/#website\",\"url\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/\",\"name\":\"Flow Science and Engineering\",\"description\":\"Tamer Zaki&#039;s Research Group\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/engineering.jhu.edu\\\/zaki\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Machine learning - Flow Science and Engineering","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/engineering.jhu.edu\/zaki\/research\/machine-learning\/","og_locale":"en_US","og_type":"article","og_title":"Machine learning - Flow Science and Engineering","og_description":"Evolutional Deep Neural Networks (EDNN) are a powerful new approach to solving partial differential equations (PDE). 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