physics-informed-neural-networks-for-heat-transfer

Physics-Informed Neural Networks for Heat Transfer

This example was originally hosted here.

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).

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

$$ \rho c \frac{\partial u}{\partial t} - \nabla \cdot \left(k \nabla u \right) = Q. $$

How to get started

To get started, clone this repository and run "Example_pinn.mlx".

Requirements

• MATLAB ®
• Deep Learning Toolbox ™
• Partial Differential Equation Toolbox ™

MATLAB version should be R2024a and later (Tested in R2024a).

References

[1] Raissi, Maziar, Paris Perdikaris, and George E. Karniadakis. "Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations." Journal of Computational Physics 378 (2019): 686-707.

License

The license is available in license.txt file in this GitHub repository.

Copyright (c) 2024, The MathWorks, Inc.