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Example_pinn.mlx

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README.md

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# Physics-Informed Neural Networks for Heat Transfer
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In recent years, Physics-Informed Neural Networks[1] are applied to various types of application tasks.
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This example shows how to train a neural network using data calculated with partial differential equations(PDEs), and heat equation as loss function to predict temperature distributions.
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In recent years, Physics-Informed Neural Networks[1] have been applied to various types of application tasks.
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This example shows how to train a neural network to predict temperature distributions given new initial and boundary conditions. The neural network was trained using a loss function that includes a data loss component, which measures the discrepancy between the network's predictions and targets derived from finite element simulations, as well as a physics-informed loss component that evaluates the residual of the governing partial differential equation (PDE).
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<img src="https://github.com/matlab-deep-learning/Physics-Informed-Neural-Networks-for-Heat-Transfer/blob/main/ref_images/Results.png" width="720">
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<img src="https://insidelabs-git.mathworks.com/tfukumot/physics-informed-neural-networks-for-heat-transfer/-/raw/main/ref_images/Results.png" width="720">
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Here is the Heat equation used in loss function
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The PDE used in the loss function is the transient heat equation:
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<img src="https://github.com/matlab-deep-learning/Physics-Informed-Neural-Networks-for-Heat-Transfer/blob/main/ref_images/HeatEquation.png" width="360">
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<img src="https://insidelabs-git.mathworks.com/tfukumot/physics-informed-neural-networks-for-heat-transfer/-/raw/main/ref_images/HeatEquation.png" width="360">
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## **How to get started**
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To get started, clone this repository and run "Example_pinn.mlx".
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## **Requirements**
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## **License**
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The license is available in license.txt file in this GitHub repository.
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## Author:
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![Image of MATLAB](http://www.mathworks.com/includes_content/nextgen/images/bg_header_mwlogo_notag.jpg)
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### Takuji Fukumoto
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Product Marketing, MathWorks
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### Ben Wells-Day
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Language of Tech. Computing, MathWorks
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Copyright (c) 2024, The MathWorks, Inc.
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