{"page":"\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/resources-c03aa079.css\" /\u003e\n\u003clink rel=\"stylesheet\" href=\"https://lessonplanet.com/assets/packs/css/lp_boclips_stylesheets-517835be.css\" media=\"all\" /\u003e\n\u003cdiv data-title='Physics-Informed Neural Network' data-url='/boclips/videos/627db6542558ce206dd59eba' data-video-url='/boclips/videos/627db6542558ce206dd59eba' id='bo_player_modal'\u003e\n\u003cdiv class='boclips-resource-page modal-dialog panel-container'\u003e\n\u003cdiv class='react-notifications-root'\u003e\u003c/div\u003e\n\u003cdiv class='rp-header'\u003e\n\u003cdiv class='rp-type'\u003e\n\u003ci aria-hidden='true' class='fai fa-regular fa-circle-play'\u003e\u003c/i\u003e\nVideo\n\u003c/div\u003e\n\u003ch1 class='rp-title' id='video-title'\u003e\nPhysics-Informed Neural Network\n\u003c/h1\u003e\n\u003cdiv class='rp-actions'\u003e\n\u003cdiv class='mr-1'\u003e\n\u003ca class=\"btn btn-success\" data-posthog-event=\"Signup: LP Signup Activity\" data-posthog-location=\"body_link_boclips\" data-remote=\"true\" href=\"/subscription/new\"\u003e\u003cspan\u003e\u003cspan\u003eGet Free Access\u003c/span\u003e\u003cspan class=\"\"\u003e for 10 Days\u003c/span\u003e\u003cspan\u003e!\u003c/span\u003e\u003c/span\u003e\u003c/a\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-body'\u003e\n\u003cdiv class='rp-info'\u003e\n\u003cdiv aria-label='Hide resource details' class='rp-hide-info' role='button' tabindex='0'\u003e\u0026times;\u003c/div\u003e\n\u003ci aria-label='Expand resource details' class='rp-expand-info fai fa-solid fa-up-right-and-down-left-from-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003ci aria-label='Compress resource details' class='rp-compress-info fai fa-solid fa-down-left-and-up-right-to-center' role='button' tabindex='0'\u003e\u003c/i\u003e\n\u003cdiv class='rp-rating'\u003e\n\u003cspan class='resource-pool'\u003e\n\u003cspan class='pool-label'\u003ePublisher:\u003c/span\u003e\n\u003cspan class='pool-name'\u003e\n\u003cspan class='text'\u003e\u003ca data-publisher-id=\"30355135\" href=\"/search?publisher_ids%5B%5D=30355135\"\u003eAPMonitor\u003c/a\u003e\u003c/span\u003e\n\u003c/span\u003e\n\u003c/span\u003e\n\u003c/div\u003e\n\u003cdiv class='rp-description'\u003e\n\u003cspan class='short-description'\u003ePhysics-based information is integrated into the Neural Network architecture with the use of constraints or other relationships such as periodic cycles. Empirical regression has limitations, especially when predictions are requested...\u003c/span\u003e\n\u003cspan class='full-description hide'\u003ePhysics-based information is integrated into the Neural Network architecture with the use of constraints or other relationships such as periodic cycles. Empirical regression has limitations, especially when predictions are requested outside of the training region. Physics-based information can overcome this limitation by including fundamental engineering knowledge such as constraints during the training process.\u003cbr/\u003e\u003cbr/\u003eBackground: Parachor values are a factor in the prediction of several thermophysical properties such as surface tension and thermal conductivity. The parachor value (P) is used to predict surface tension with the difference between the density of saturated liquid.\u003cbr/\u003e\u003cbr/\u003eSurface tension and thermal conductivity are two specific properties that need improved predictions. A more accurate predictor of the parachor value (P) is an important step to improve those thermophysical properties. Most deep learning methods use a limited set of activation functions (ReLU, sigmoid, tanh, and linear) and perform unconstrained regression to minimize a loss function. The purpose of this case study is to explore the addition of physics-based information in the fitting process. This may include the use of new types of activation functions or constraints on the adjustable weights. The data for this case study is from Gharagheizi, et. al. (2011) who explored deep learning (a multi-layered neural network) to improve parachor predictions for 277 compounds from 40 functional groups.\u003cbr/\u003e\u003cbr/\u003eObjective: Develop a prediction of the parachar from the chemical compound data set. Report the correlation coefficient (R2) for predicting Parachor in the test set. Randomly select values that split the data into a train (80%) and test (20%) set. Use Linear Regression and Neural Network (Deep Learning) with and without constraints. There is additional information on adding constraints to linear regression (see Gekko example) and to the neural network weights. For the constrained cases, enforce a positive parachor contribution for each group. 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