Interpreting Heat Wave Equation using IBM Granite

Project Overview

The project generates heat equation solution using Finite Element Analysis. This data is used to finetune IBM Granite to interpret heat equation solutions (given in a .vtk format file).

Data Generation

Methodology

• Finite Element Method for data generation
• Unit square grid: 25 x 25 points
• 30 different .vtk files generated
• 4 questions per file, totaling 120 questions

Detailed Questions Used for data generation

1. Corner Temperature Inquiry

   Analyze the given steady-state heat equation solution, saved in the format:
   Coordinates (x,y): Temperature at (x,y)
   And then tell - What is the temperature distribution at the corner (0, 0) of the unit square mesh?
   

2. X-Axis Temperature Variation

   Analyze the given steady-state heat equation solution, saved in the format:
   Coordinates (x,y): Temperature at (x,y)
   And then tell - How does the temperature change with respect to the position along the x-axis at y = 0.5?
   

3. Maximum Temperature Location

   Analyze the given steady-state heat equation solution, saved in the format:
   Coordinates (x,y): Temperature at (x,y)
   And then tell at what coordinates does the maximum temperature occur.
   

4. Temperature Decay Analysis

   Analyze the given steady-state heat equation solution, saved in the format:
   Coordinates (x,y): Temperature at (x,y)
   And then tell - What can you infer about the decay rate of temperature?
   

The given code was used to generate relevant responses -

def solve(temp):
    answers = [
        f"The answer is {get_temperature(temp, 0.0, 0.0)}.",
        f"The answer is {temp[np.isclose(temp['y'], 0.5, atol=1e-2)]['Temperature'].mean()}.",
        f"The answer is {temp.loc[temp['Temperature'].idxmax(), 'x'], temp.loc[temp['Temperature'].idxmax(), 'y']}.",
        "The decay rate of temperature seems constant since the information about time is not given."
    ]
    return answers

The training data can be found here - training_data. This dataset was later used to combine vtk data and prompts/questions to make vtk_training_data.csv

Fine-Tuning Pipeline

Approach

• Create DataFrame with prompts and responses
• Prepare data for LLM fine-tuning

Notebooks

1. heat-wave-equation-data-generation.ipynb: Data generation
2. interpreting-heat-wave-equation-using-llm.ipynb: LLM fine-tuning pipeline