https://github.com/314arhaam/heat-pinn

A Physics-Informed Neural Network to solve 2D steady-state heat equations.
https://github.com/314arhaam/heat-pinn

chemical-engineering deep-learning finite-difference heat-equation heat-transfer machine-learning partial-differential-equations physics physics-informed-ml physics-informed-neural-networks process-engineering python3

Last synced: 5 days ago
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A Physics-Informed Neural Network to solve 2D steady-state heat equations.

Host: GitHub
URL: https://github.com/314arhaam/heat-pinn
Owner: 314arhaam
License: mit
Created: 2021-11-12T16:06:33.000Z (over 4 years ago)
Default Branch: main
Last Pushed: 2026-05-25T01:56:58.000Z (19 days ago)
Last Synced: 2026-05-25T03:25:01.740Z (19 days ago)
Topics: chemical-engineering, deep-learning, finite-difference, heat-equation, heat-transfer, machine-learning, partial-differential-equations, physics, physics-informed-ml, physics-informed-neural-networks, process-engineering, python3
Language: Jupyter Notebook
Homepage:
Size: 2.23 MB
Stars: 182
Watchers: 5
Forks: 25
Open Issues: 1
Metadata Files:
- Readme: README.md
- License: LICENSE

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[![CI](https://github.com/314arhaam/heat-pinn/actions/workflows/ci.yml/badge.svg)](https://github.com/314arhaam/heat-pinn/actions/workflows/ci.yml)

[![Validation-CPU](https://github.com/314arhaam/heat-pinn/actions/workflows/validation.yml/badge.svg)](https://github.com/314arhaam/heat-pinn/actions/workflows/validation.yml)

# Heat-PINN

 A Physics-Informed Neural Network, to solve 2D steady-state heat equation based on the methodology, introduced in: Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations. 
  

## **Table of Contents**

 - [Introduction](#intro)

 - [Results](#res)

## Introduction 

In this project, a PINN is trained to solve a 2D heat equation and the final results is compared to a solution based on FDM method. 

For more detailts about the project read [this](https://github.com/314arhaam/burger-pinn).

### Problem

The governing equation:  

$$

\Theta = \frac{T - T_{\textbf{min}}}{T_{\textbf{max}}-T_{\textbf{min}}}

$$   

$$ 

\nabla^2{\Theta} = (\partial_{xx}+\partial_{yy})\Theta=0

$$  

in the following domain:  

  

$$  

D = \\{ (x, y)|-1\le x \le +1 \land -1\le y \le +1 \\}

$$  

With the following boundary conditions:

  

$$

\begin{equation}

  \begin{cases}

    T(-1, y) = 75.0 \degree{C}\\

    T(+1, y) = 0.0 \degree{C}\\

    T(x, -1) = 50.0 \degree{C}\\  

    T(x, +1) = 0.0 \degree{C}\\

  \end{cases}

\end{equation}

$$  

  

When normalized:  

$$

\begin{equation}

  \begin{cases}

    \Theta(-1, y) = 1\\

    \Theta(+1, y) = 0\\

    \Theta(x, -1) = \frac{2}{3}\\  

    \Theta(x, +1) = 0\\

  \end{cases}

\end{equation}

$$

## Heat-PINN CLI

### Installation

### Build

```

.-----------------------------------------------------------------------.

|.##.....#.#######....###...#######........########.###.##....#.##....##|

|.##.....#.##........##.##.....##..........##.....#..##.###...#.###...##|

|.##.....#.##.......##...##....##..........##.....#..##.####..#.####..##|

|.########.######..##.....#....##...######.########..##.##.##.#.##.##.##|

|.##.....#.##......########....##..........##........##.##..###.##..####|

|.##.....#.##......##.....#....##..........##........##.##...##.##...###|

|.##.....#.#######.##.....#....##..........##.......###.##....#.##....##|

'-----------------------------------------------------------------------'

usage: heat build [-h] [--in-shape IN_SHAPE] [--out-shape OUT_SHAPE]

                  [--n-hidden-layers N_HIDDEN_LAYERS]

                  [--neuron-per-layer NEURON_PER_LAYER] [--actfun ACTFUN]

                  [--name NAME]

options:

  -h, --help            show this help message and exit

  --in-shape IN_SHAPE   Shape of the input tensor to feed into NN. Equal to

                        the number of independent variables of PDE.

  --out-shape OUT_SHAPE

                        Shape of the output tensor of NN. For heat transfer

                        it's T (equal to 1)

  --n-hidden-layers N_HIDDEN_LAYERS

                        Number of hidden layers in the NN

  --neuron-per-layer NEURON_PER_LAYER

                        Number of neurons in each hidden layer

  --actfun ACTFUN       Activation function

  --name NAME           Name of the model.

```

### Train

```

.-----------------------------------------------------------------------.

|.##.....#.#######....###...#######........########.###.##....#.##....##|

|.##.....#.##........##.##.....##..........##.....#..##.###...#.###...##|

|.##.....#.##.......##...##....##..........##.....#..##.####..#.####..##|

|.########.######..##.....#....##...######.########..##.##.##.#.##.##.##|

|.##.....#.##......########....##..........##........##.##..###.##..####|

|.##.....#.##......##.....#....##..........##........##.##...##.##...###|

|.##.....#.#######.##.....#....##..........##.......###.##....#.##....##|

'-----------------------------------------------------------------------'

usage: heat train [-h] [--domain DOMAIN] [--boundary BOUNDARY] [--model MODEL]

                  [-l LR] [--epochs EPOCHS] [--every EVERY]

options:

  -h, --help            show this help message and exit

  --domain DOMAIN       Path of domain data file

  --boundary BOUNDARY   Path of boundary data file

  --model MODEL         Path of model file

  -l LR, --lr LR, --learning-rate LR

                        Learning rate for the optimizer

  --epochs EPOCHS       Number of training epochs

  --every EVERY         Print result for every n epochs

```

### Inference

```

.-----------------------------------------------------------------------.

|.##.....#.#######....###...#######........########.###.##....#.##....##|

|.##.....#.##........##.##.....##..........##.....#..##.###...#.###...##|

|.##.....#.##.......##...##....##..........##.....#..##.####..#.####..##|

|.########.######..##.....#....##...######.########..##.##.##.#.##.##.##|

|.##.....#.##......########....##..........##........##.##..###.##..####|

|.##.....#.##......##.....#....##..........##........##.##...##.##...###|

|.##.....#.#######.##.....#....##..........##.......###.##....#.##....##|

'-----------------------------------------------------------------------'

usage: heat infer [-h] [--data DATA] [--model MODEL] [--output OUTPUT]

options:

  -h, --help       show this help message and exit

  --data DATA      Path of data file to perform inference

  --model MODEL    Path of model file

  --output OUTPUT  Path of output data file

```

## Validation 

  

### Square geometry 



  

 

Temperature profiles:  



  



## Results 

### Doughnut geometry



  



### Screw 



  



### Connecting Rod



  



### Gear geometry



  





  



## Performance Comparison

Results obtained from a [9 layered DNN](https://github.com/314arhaam/heat-pinn/blob/main/assets/model_plot.png) (1000 epochs) and FDM code on a 100×100 grid. The FDM code is written in Python.

|**Method**|**Computation time (s)**|

|-|-|

|PINN|66.35|

|FDM|77.60|

## Note

This implementation is based on [Tensorflow 2.0](https://www.tensorflow.org/guide/effective_tf2) package and made possible by [Google Colabratory](https://colab.research.google.com) GPU.

ecosyste.ms

Data

Tools

Indexes

Applications

Experiments

Awesome

https://github.com/314arhaam/heat-pinn

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