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tfukumot committed Sep 17, 2024
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In recent years, Physics-Informed Neural Networks[1] have been applied to various types of application tasks.
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).

<img src="https://insidelabs-git.mathworks.com/tfukumot/physics-informed-neural-networks-for-heat-transfer/-/raw/main/ref_images/Results.png" width="720">
<img src="https://github.com/matlab-deep-learning/physics-informed-neural-networks-for-heat-transfer/blob/main/ref_images/Results.png" width="720">

The PDE used in the loss function is the transient heat equation:

<img src="https://insidelabs-git.mathworks.com/tfukumot/physics-informed-neural-networks-for-heat-transfer/-/raw/main/ref_images/HeatEquation.png" width="360">
<img src="https://github.com/matlab-deep-learning/physics-informed-neural-networks-for-heat-transfer/blob/main/ref_images/HeatEquation.png" width="360">


## **How to get started**
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## **License**
The license is available in license.txt file in this GitHub repository.

## **Open in MATLAB Online**
[![Open in MATLAB Online](https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg)](https://matlab.mathworks.com/open/github/v1?repo=matlab-deep-learning/Physics-Informed-Neural-Networks-for-Heat-Transfer)

Copyright (c) 2024, The MathWorks, Inc.

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