poromat

A Python package for modeling stress–strain behavior of porous titanium alloys under various strain rates and temperatures, based on extremely limited experimental data.

Project Summary

This project constructs global stress–strain prediction models for porous Ti alloys using only 38 sets of uniaxial compression tests. Guided by the Zener–Arrhenius (ZA) constitutive framework, I implement three regression approaches and evaluate them using a Leave-One-Porosity-Out (LOPO) framework. Generalization performance is statistically compared via Friedman and Nemenyi tests. Meta-learning shows advantages on unseen porosity conditions.

Dataset Structure

Porosity 26%

├── 25°C:  [1200, 2300, 3600, 5200]  
├── 100°C: [950, 2200, 3000, 4200]  
├── 200°C: [1050, 1500, 1950, 2800, 3800]  
└── 300°C: [1100, 1900, 2900, 3700]  

Porosity 36%

├── 25°C:  [1000, 2000, 3000]  
├── 100°C: [1300, 2050, 2350, 3400, 3700]  
└── 300°C: [1000, 2000, 3000, 4000, 4500]  

Data Source:

Liu, Z., Ji, F., Wang, M., & Zhu, T. (2017).
One-Dimensional Constitutive Model for Porous Titanium Alloy at Various Strain Rates and Temperatures. Metals, 7(1), 24.
https://doi.org/10.3390/met7010024

Regression Methods

1. Adaboost + Decision Tree (Smoothed)
   Custom interpolator with smoothing, performing interpolation across strain rate, temperature, and porosity dimensions.

2. LightGBM
   Gradient boosting regression on standardized features, trained directly on the limited dataset.

3. Meta-learning (MAML)
   Two hidden layers (see code) trained using learn2learn for fast adaptation to new porosity conditions.
   Supports credible intervals via MC Dropout.

All the pre-trained models are saved in Release v0.1.2-models.

Model Comparison

I conducted three rounds of Leave-One-Porosity-Out (LOPO) experiments, each time holding out one porosity level for testing.

Statistical Evaluation

Model performance was compared using the Friedman test, followed by the Nemenyi post-hoc test. Evaluation Result

• Null Hypothesis (H₀): All models have equal performance (no significant difference).
• Alternative Hypothesis (H₁): At least one model performs significantly differently from the others.
• Significance Level (α): 0.05

• No model showed statistically significant superiority (p > 0.05).
• However, ranking metrics consistently favored meta-learning on unseen porosity conditions.
• Due to only 3 porosity groups, statistical power is limited.

Recommendation

Based on both performance trends and materials knowledge:

• Meta-learning captures more nonlinearity and adapts better to new porosity conditions.
• Interpolation performs similarly and is easier to interpret.

Installation and Model File Setup

Environment Setup: This project requires Python 3.10.

pip install poromat

The .pkl and .csv files are required to run predictions and are not included in the PyPI package.

You can download them using:

import poromat
poromat.download_data()
poromat.download_all_models()

Quick Start

import poromat
poromat.download_all_models() # You need to download the models

poromat.plot(16, 300, 3300, step=0.002, method="meta")

poromat.save_csv(16, 300, 3000, step=0.002, method="meta")

strain, stress, stress_lower, stress_upper = poromat.generate_prediction(
    model_name="meta",
    porosity=16,
    T=300,
    rate=3000,
    show_plot=True
)

Key Functions

Purpose

Designed for materials scientists studying porous titanium alloys.
This tool enables fast and flexible access to mechanical response predictions under varying testing conditions, helping reduce the need for costly and time-consuming mechanical experiments.

Developer

Yun Zhou (Robbie)
Background in Mechanical Engineering and Applied Data Science.
Email: robbiezhou1@gmail.com GitHub: @Green-zy