Inverse Heat Equation

This project contains scripts to run experiments for solving the inverse problem in heat equation to reconstruct thermal conductivity from temperature measurements using different sensor configurations.

Prerequisites

Ensure you have the following dependencies installed:

• Python 3.11+
• torch
• torchvision
• torchdiffeq
• numpy
• pandas
• plotly
• argparse
• moviepy

Running the Experiment

To run the test2D-typewriter.py script, use the following command:

python test/test2D-typewriter.py --experiment <experiment_index> --epochs <number_of_epochs> --sensor-type <sensor_type> --num-static-sensors <number_of_static_sensors>

Arguments

• experiment: The index of the experiment in the training set (default: 0).
• epochs: The number of epochs for training (default: 500).
• sensor-type: The type of sensors to use, either "moving" (4 sensors) or "static".
• num-static-sensors: The number of static sensors to use (16 or 64), only applicable if sensor-type is "static" (default: 16).

Example

To run an experiment with the default settings:

python test/test2D-typewriter.py --experiment 0 --epochs 500 --sensor-type moving

To run an experiment with static sensors:

python test/test2D-typewriter.py --experiment 1 --epochs 1000 --sensor-type static --num-static-sensors 64

Understanding the output

The script will generate the following outputs:

• PNG frames for each epoch and forward simulation.
• CSV files containing the basis, gradient, loss, and error data in the log/data/<config> directory.
• Video files combining forward and inverse processes in the log/video/<config> directory.
• PDF images of the forward and epoch results in the log/image/<config> directory.

The outputs will be saved in the log and tmp directories.

Notes

• Ensure the data directory contains the necessary datasets (MNIST).
• Adjust memory limits if necessary using the resource module in the script.

For more details, refer to the comments and documentation within the src/inverse_heat2D.py and test/test2D-typewriter.py script.