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\nPhysics-Informed Neural Network\n

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\nPhysics-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...\nPhysics-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.

Background: 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.

Surface 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.

Objective: 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. Discuss the performance of each on the train and test sets.
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Resource Details

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Media Length
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21:58
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Grade
10th - Higher Ed
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Subjects
Social Studies & History
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Media Type
Instructional Videos
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Source:
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\nAPMonitor.com\n\n
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Date
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2022
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Language
English
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For Teacher Use
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Fine Print: Educational Use
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Concepts

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surface tension, linear regression, values
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Additional Tags

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apmonitor, pinns, physics, fundamentals, machine learning, hyperbolic tangent, absolute air, jupiter notebook, absolute error, neural network, sample points, parity plot, parameter weights, google colab, squared error, case study, negative values, add constraints, training data, regression, weights, output, approach, case, measured, worse, model, training, gecko, predicted
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