├── pinn_pre.mat ├── Condition.xlsx ├── Example_pinn.mlx ├── ref_images ├── Thumbs.db ├── Results.png ├── HeatEquation.png └── LearningCurve.png ├── SECURITY.md ├── license.txt └── README.md /pinn_pre.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/matlab-deep-learning/Physics-Informed-Neural-Networks-for-Heat-Transfer/HEAD/pinn_pre.mat -------------------------------------------------------------------------------- /Condition.xlsx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/matlab-deep-learning/Physics-Informed-Neural-Networks-for-Heat-Transfer/HEAD/Condition.xlsx -------------------------------------------------------------------------------- /Example_pinn.mlx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/matlab-deep-learning/Physics-Informed-Neural-Networks-for-Heat-Transfer/HEAD/Example_pinn.mlx -------------------------------------------------------------------------------- /ref_images/Thumbs.db: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/matlab-deep-learning/Physics-Informed-Neural-Networks-for-Heat-Transfer/HEAD/ref_images/Thumbs.db -------------------------------------------------------------------------------- /ref_images/Results.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/matlab-deep-learning/Physics-Informed-Neural-Networks-for-Heat-Transfer/HEAD/ref_images/Results.png -------------------------------------------------------------------------------- /ref_images/HeatEquation.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/matlab-deep-learning/Physics-Informed-Neural-Networks-for-Heat-Transfer/HEAD/ref_images/HeatEquation.png -------------------------------------------------------------------------------- /ref_images/LearningCurve.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/matlab-deep-learning/Physics-Informed-Neural-Networks-for-Heat-Transfer/HEAD/ref_images/LearningCurve.png -------------------------------------------------------------------------------- /SECURITY.md: -------------------------------------------------------------------------------- 1 | # Reporting Security Vulnerabilities 2 | 3 | If you believe you have discovered a security vulnerability, please report it to 4 | [security@mathworks.com](mailto:security@mathworks.com). Please see 5 | [MathWorks Vulnerability Disclosure Policy for Security Researchers](https://www.mathworks.com/company/aboutus/policies_statements/vulnerability-disclosure-policy.html) 6 | for additional information. -------------------------------------------------------------------------------- /license.txt: -------------------------------------------------------------------------------- 1 | Copyright (c) 2024, The MathWorks, Inc. 2 | All rights reserved. 3 | 4 | Redistribution and use in source and binary forms, with or without 5 | modification, are permitted provided that the following conditions are 6 | met: 7 | 8 | * Redistributions of source code must retain the above copyright 9 | notice, this list of conditions and the following disclaimer. 10 | * Redistributions in binary form must reproduce the above copyright 11 | notice, this list of conditions and the following disclaimer in 12 | the documentation and/or other materials provided with the distribution 13 | * Neither the name of the The MathWorks, Inc. nor the names 14 | of its contributors may be used to endorse or promote products derived 15 | from this software without specific prior written permission. 16 | 17 | THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 18 | AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 19 | IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 20 | ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 21 | LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 22 | CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 23 | SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 24 | INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 25 | CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 26 | ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 27 | POSSIBILITY OF SUCH DAMAGE. 28 | 29 | 30 | 31 | 32 | 33 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | :warning: Project Archived 2 | 3 | This repository is no longer actively maintained. 4 | 5 | Development has moved to a new repository, which contains all the content from here and is actively updated with new features and improvements. 6 | 7 | ➡️ Please visit [physics-informed-neural-networks-for-heat-transfer](https://github.com/matlab-deep-learning/SciML-and-Physics-Informed-Machine-Learning-Examples/tree/main/physics-informed-neural-networks-for-heat-transfer) for the latest version and continued development. 8 | 9 | This repository will remain available for existing users, but we recommend switching to the new repository for the most up-to-date experience. 10 | 11 | # Physics-Informed Neural Networks for Heat Transfer 12 | 13 | 14 | In recent years, Physics-Informed Neural Networks[1] have been applied to various types of application tasks. 15 | 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). 16 | 17 | 18 | 19 | The PDE used in the loss function is the transient heat equation: 20 | 21 | 22 | 23 | 24 | ## **How to get started** 25 | To get started, clone this repository and run "Example_pinn.mlx". 26 | 27 | 28 | ## **Requirements** 29 | - [MATLAB ®](https://jp.mathworks.com/products/matlab.html) 30 | - [Deep Learning ToolboxTM](https://jp.mathworks.com/products/deep-learning.html) 31 | - [Partial Differential Equation ToolboxTM](https://www.mathworks.com/products/pde.html) 32 | 33 | 34 | MATLAB version should be R2024a and later (Tested in R2024a) 35 | 36 | ## **References** 37 | 38 | [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. 39 | 40 | ## **License** 41 | The license is available in license.txt file in this GitHub repository. 42 | 43 | ## **Open in MATLAB Online** 44 | [![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) 45 | 46 | Copyright (c) 2024, The MathWorks, Inc. 47 | 48 | 49 | --------------------------------------------------------------------------------