phy-gpr

Hierarchical physics-informed Gaussian process regression for yield strength prediction in laser powder bed fusion.

Overview

This repository contains a research pipeline for modeling the relationship between laser powder bed fusion process parameters and mechanical response using Gaussian process regression (GPR).

The workflow is organized into three main stages:

1. Learn intermediate structure descriptors from process parameters.
2. Transform those descriptors via Hall-Petch and porosity-strength relations and use them inside a physics-informed GPR model for strength prediction.
3. Solve an inverse design problem to search for process parameters that match target strength values.

Illustration of hierarchical physics-informed Gaussian process regression for yield strength prediction.

The datasets for training are sourced from Luo et al. (https://www.sciencedirect.com/science/article/pii/S2214860422003128) and (https://www.sciencedirect.com/science/article/abs/pii/S2214860423004177.)

An additional ablation script is included to compare baseline and physics-informed variants.

What The Pipeline Does

The project uses laser power P and scan speed v as inputs.

Step 1 predicts latent or intermediate material descriptors:

• grain size d
• porosity phi

Step 2 predicts yield strength YS with two model families:

• a baseline GP using only process parameters
• a physics-informed GP that propagates Step 1 descriptor uncertainty into the final prediction

Step 3 performs inverse optimization over (P, v) to match held-out target YS values.

Step 4 runs ablations to compare:

• untuned baseline GP
• tuned baseline GP
• full physics-informed GP
• tuned physics-informed GP
• Hall-Petch-only variant
• porosity-only variant

Data

The current pipeline reads source data from:

• data/AlSi10Mg PSP feature table.xlsx

The data preparation code currently:

• reads 32 valid rows from the spreadsheet
• extracts process parameters and summary statistics
• uses Gaussian sampling to expand each original row into 100 synthetic samples
• splits train and test sets by original group id, not by individual augmented rows

Repository Layout

phy-gpr/
├── data/
│   ├── AlSi10Mg PSP feature table.xlsx
│   └── Ti-6Al-4V PSP feature table.xlsx
├── outputs/
├── run_pipeline.py
├── run_ablations.py
└── src/
    ├── data_prep.py
    ├── step1_gpr.py
    ├── step2_gpr.py
    ├── step3_optim.py
    ├── step4_ablations.py
    └── utils.py

Environment

This project is written in Python and uses common scientific computing packages.

At minimum, you should install dependencies equivalent to:

pip install numpy pandas scipy scikit-learn matplotlib openpyxl

If you want reproducible isolated setup, a virtual environment is recommended:

python -m venv .venv
source .venv/bin/activate
pip install numpy pandas scipy scikit-learn matplotlib openpyxl

How To Run

Main Pipeline

python run_pipeline.py

This script is intended to run:

1. data preparation
2. Step 1 dual GPR for d and phi
3. Step 2 physics-informed GPR for YS
4. Step 3 inverse optimization

Ablation Study

python run_ablations.py

Optional arguments:

python run_ablations.py --test-groups 6 --baseline-restarts 10 --physics-restarts 10

Outputs

Generated artifacts are written to outputs/.

These outputs cover:

• train and test metrics
• prediction plots
• process-parameter response maps
• optimization convergence traces
• serialized model artifacts