EvoPINN: An Evolutionary Physics-Informed Neural Network Framework

EvoPINN is a hybrid machine learning framework that integrates Physics-Informed Neural Networks (PINNs) with traditional Artificial Neural Networks (ANNs) to model complex physical phenomena.We utlize it to Predict the Collapse Potential in Chemically Stabilized Unsaturated Gypseous Soils, while simultaneously embedding physical constraints into the learning process.

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Overview

The EvoPINN framework is designed to:

• Leverage PINNs for optimizing neural network structures.
• Incorporate Physics-Informed Neural Networks to enforce known physical laws through custom loss functions.
• Uses Artificial Neural Networks to model relationships in datasets involving partial knowledge or observational data.
• Evaluated performance using standard regression metrics like RMSE and R² Score.

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Features

• Physics Neural Architecture Search (ENAS) for PINNs
• Physics-based loss enforcement in training
• Scalable to both low- and high-dimensional regression problems
• Easy to integration with PyTorch and DEAP

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Piplines

📁 Directory Structure

├── data/
│   ├── cp.csv
│── Notebooks/ 
│   ├── Inference_pd_pinns_exp2_2ice_2.ipynb 
│   ├── pd_pinns_exp2_2ice_2.ipynb
│   ├── pd_pinns_exp2_2ice_2_draft_exp.ipynb
│   └── regression&gauss_markov_assumptions.ipynb
│── Inference_pd_pinns_exp2_2ice_2.ipynb 
│── pd_pinns_exp2_2ice_2.ipynb
│── pd_pinns_exp2_2ice_2_draft_exp.ipynb
│── regression&gauss_markov_assumptions.ipynb

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Dataset

The collocted dataset are avaliable under data/dataset.csv dir., Please if want to use it cite it as mentioned below

Installation

pip install -r requirements.txt
torch
numpy
pandas
scikit-learn
matplotlib
seaborn
openpyxl
deap

Usage

We can follow the instruction below to either train(for reproduce) or test(for usage or validate) or we can use Google Colab Notebook listed under Notebooks dir.

Training

git clone https://github.com/Mohammed20201991/EvoPINN.git
cd EvoPINN
python pd_pinns_exp2_2ice_2.py --data "path/to/data"

Testing

python Inference_pd_pinns_exp2_2ice_2.py --data "path/to/data"

Results

Performance Metrics Comparison

The proposed Physics-Informed Neural Network (PINNs) significantly outperformed conventional statistical regression models in predicting the collapse potential of chemically stabilized unsaturated gypseous soils.

Metric	PINNs (Ours)	LR (OLS)	Lasso Regression	Ridge Regression	Physics-Constrained Random Forest	MLPNN (Previous Study)	RBFN (Previous Study)
RMSE	1.4109	9.9367	9.9367	10.0214	3.8173	1.119	1.731
R²	0.9896	0.609	0.609	0.603	0.9098	0.904	0.841
Dataset Size	600 samples	-	-	-	-	766 samples	766 samples

Legend:

• PINNs: Physics-Informed Neural Networks
• LR (OLS): Linear Regression (Ordinary Least Squares)
• RL: Ridge Regression
• RR: Regularized Regression

📈 Lower RMSE and higher R² indicate better model performance.

Key Findings

✅ PINNs achieved an R² of 0.9896, substantially outperforming all traditional regression models.
✅ RMSE was reduced by over 85% compared with Linear, Lasso, and Ridge Regression.
✅ The proposed approach achieved superior prediction accuracy while using 600 samples, demonstrating excellent generalization capability.
📌 Although the previous MLPNN reported a slightly lower RMSE, our proposed PINNs framework provides physics-informed interpretability, improved robustness, and significantly higher explanatory power (R² = 0.9896).

Performance Interpretation

• Lower RMSE indicates smaller prediction errors.
• Higher R² indicates better agreement between predicted and measured collapse potential.

Publication

🎉 This work has been accepted for publication in the Springer Nature journal:

Modeling Earth Systems and Environment

https://link.springer.com/journal/40808

Paper Title

Physics-Informed Neural Networks for Predicting Collapse Potential in Chemically Stabilized Unsaturated Gypseous Soils: Interpretable Machine Learning Framework

Cite this article

Jasim, O.H., Al-Hitawi, M.A.S., Fattah, M.Y. et al. Physics-informed neural networks for predicting collapse potential in chemically stabilized unsaturated gypseous soils: interpretable machine learning framework.
Model. Earth Syst. Environ. 12, 219 (2026). https://doi.org/10.1007/s40808-026-02853-1

@misc{evopinn2025,
  title        = {Physics-Informed Neural Networks for Predicting Collapse Potential in Chemically Stabilized Unsaturated Gypseous Soils: Interpretable Machine Learning Framework},
  author       = {Omer K. Jassim, Mohammed A.S. Al-Hitawi, et.al },
  year         = {2025},
  publisher    = {Springer Nature},
  journal      = {Modeling Earth Systems and Environment},
  email        = {al_hitawe@uofallujah.edu.iq}
  howpublished = {\url{https://github.com/Mohammed20201991/EvoPINN}},
}