Supplementary Material for ICLR 2026 Submission
Paper Title: Beyond Euler: An Explainable Machine Learning Framework for Predicting and Interpreting Buckling Instabilities in Non-Ideal Materials

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This zip file contains the source code and data for the experiments described in the paper.

## CONTENTS:
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1. buckling_analysis.py: The Python script used for data loading, feature engineering, model training (5-fold cross-validation), and generating the SHAP analysis plots.
2. buckling_dataset.csv: The full dataset of 147 experimental measurements used in the paper. Columns include length, diameter, and critical load.
3. README.txt: This file.

## HOW TO RUN:
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The script can be run directly from the terminal. Ensure all required libraries are installed.

Command:
python buckling_analysis.py

Expected Output:
The script will print the average R-squared and RMSE metrics to the console after running the cross-validation. It will also generate and save the two main figures from the paper ('predicted_vs_actual.png' and 'shap_summary_plot.png') in the same directory.

## REQUIREMENTS:
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- Python 3.8+
- pandas
- scikit-learn
- xgboost
- shap
- matplotlib