PGNN: Innovative Applications of Physics-Guided Neural Networks in Materials Science

Core Guide to the PGNN-Al6011-Hot-Deformation Project

Project Background: Against the dilemma of insufficient accuracy of traditional physical models and lack of interpretability of pure data-driven models in predicting flow stress of aluminum alloy hot deformation, this project proposes a Physics-Guided Neural Network (PGNN) solution. Core Innovation: Combine physical equations (Arrhenius equation) with deep learning, allowing neural networks to learn interpretable physical parameters (α, n, Q, lnA), balancing prediction accuracy and physical interpretability. Basic Information:

• Original Authors: Nguyen Tran Quang Minh, Tran Ngoc Dung (Dalian University of Technology)
• Source: GitHub (Link)
• Release Date: May 29, 2026

Dilemmas in Materials Science Modeling

In metal hot deformation processes, flow stress prediction is key to optimizing processing parameters, but it faces two major challenges:

1. Traditional physical models (e.g., Arrhenius equation): Have clear physical meaning but struggle to describe complex micro-mechanisms, leading to limited precision.
2. Pure data-driven models (e.g., ANN): Have high prediction accuracy but are essentially "black boxes" and cannot explain the physical reasons for material behavior. This contradiction has driven the development of Physics-Informed Neural Networks (PINNs), and the PGNN project is the practice of this concept in the field of aluminum alloy hot deformation.

Core Design of PGNN: Neural Network Embedded with Physical Priors

Core Idea: Instead of directly predicting flow stress, let the neural network learn 4 key physical parameters:

• α (stress multiplier): Reflects the material's sensitivity to stress
• n (stress exponent): Embodies the characteristics of deformation mechanisms
• Q (activation energy): Energy barrier for thermal activation processes
• ln(A) (logarithm of pre-exponential factor): Related to deformation frequency Process: Input (temperature, strain rate, strain) → Neural network backbone → Parameter output → Arrhenius equation → Flow stress prediction. Constraint Mechanisms:
• Sigmoid activation function: Limits parameters to physically reasonable ranges.
• Physical regularization loss (λA): Adds a penalty term for consistency with physical laws besides data fitting error, ensuring the physical meaning of parameters.

Experimental Validation: Dual Breakthroughs in Accuracy and Interpretability

Dataset: Al6011-O aluminum alloy hot deformation data, covering 7 temperature points (room temperature to 450°C), 3 strain rates (0.001-0.1 s⁻¹), with a total of 1982 data points. Accuracy Comparison:

Model	R²	RMSE (MPa)	AARE (%)
Traditional SCAM model	—	69.0	54.0
Black-box ANN	0.939	13.6	12.2
PGNN+λA (this paper)	0.947	12.6	7.3
Interpretability Validation:

• Q≈179 kJ/mol: Falls within the activation energy range (130-180 kJ/mol) of Al 6xxx series alloys.
• n≈5.5-8: Decreases with increasing temperature, consistent with the theory of dislocation climb mechanism.
• Compensation effect between Q and ln(A): Correlation coefficient of -0.81, consistent with known phenomena in the hot deformation field.

Technical Implementation Details

Dataset:

• Source: High-temperature tensile tests, downsampled at Δε=0.005 intervals.
• Split: 70% training /15% validation /15% test (stratified sampling by working condition). Model Architecture: Multi-task learning structure with a shared neural network backbone +4 independent output heads (predicting α, n, Q, lnA respectively). Training Strategy:
• Optimizer: Adam
• Learning Rate: Cosine annealing scheduling
• Early Stopping: Based on validation set loss
• Hardware: Supports GPU acceleration (recommended Kaggle GPU runtime). Code Structure: The repository includes core training scripts (e.g., hot-tensil-pgnn-v6.ipynb), dataset files, comparison model implementations (SCAM/ANN), and analysis scripts.

Scientific Significance and Application Prospects

Materials Science Contributions:

• Accelerate new material development: Optimize alloy composition and process parameters.
• Digital Twin: Provide interpretable prediction models for manufacturing processes.
• Mechanism Research: Discover or verify physical laws from data. Methodological Insights:

1. Identify domain constraints: Find unbreakable physical laws.
2. Architecture Design: Embed constraints into the network structure rather than just as a loss function.
3. Interpretability Validation: Ensure learned representations align with domain knowledge. Future Outlook:

• Extend to more alloy systems and deformation conditions.
• Introduce microstructural features as input.
• Explore uncertainty quantification methods.
• Integrate into process optimization software.

Summary: The Way to Achieve Both Accuracy and Interpretability

The PGNN project proves that prediction accuracy and physical interpretability are not opposites in engineering applications. By embedding physical priors into the neural network architecture, PGNN not only surpasses the precision of traditional models but also solves the interpretability problem of black-box models. This project provides a highly valuable research example for materials modeling, manufacturing process optimization, and physics-informed machine learning fields, and is worth in-depth reference by relevant researchers and engineers.