# Citations and References

## 📚 Primary References

### **Physics-Guided Neural Networks Framework**

This project is directly inspired by the comprehensive review paper on Physics-Guided Neural Networks:

```bibtex
@misc{faroughi2023physicsguidedphysicsinformedphysicsencodedneural,
      title={Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing}, 
      author={Salah A Faroughi and Nikhil Pawar and Celio Fernandes and Maziar Raissi and Subasish Das and Nima K. Kalantari and Seyed Kourosh Mahjour},
      year={2023},
      eprint={2211.07377},
      archivePrefix={arXiv},
      primaryClass={cs.LG},
      url={https://arxiv.org/abs/2211.07377}
}
```

**Key Contributions from this Paper:**
- Comprehensive taxonomy of physics-guided neural network approaches
- Distinction between PgNNs, PiNNs, and PeNNs methodologies
- Application examples in fluid mechanics and solid mechanics
- Challenges and limitations in physics-informed machine learning

## 🌊 Fluid Mechanics References

### **Drag Coefficient Correlations**

The empirical drag coefficient formula used in this project is based on:

```bibtex
@book{white2016fluid,
  title={Fluid Mechanics},
  author={White, Frank M.},
  year={2016},
  edition={8th},
  publisher={McGraw-Hill Education},
  isbn={9780073398273}
}
```

```bibtex
@book{morrison2013introduction,
  title={An Introduction to Fluid Mechanics},
  author={Morrison, Faith A.},
  year={2013},
  publisher={Cambridge University Press},
  isbn={9781107003538}
}
```

### **Reynolds Number and Flow Regimes**

The physics-based validation across flow regimes follows established fluid mechanics principles:

```bibtex
@article{clift1978bubbles,
  title={Bubbles, drops, and particles},
  author={Clift, Roland and Grace, John R and Weber, Martin E},
  year={1978},
  publisher={Academic press}
}
```

```bibtex
@article{schlichting2000boundary,
  title={Boundary-layer theory},
  author={Schlichting, Hermann and Gersten, Klaus},
  year={2000},
  publisher={Springer}
}
```

## 🧠 Machine Learning References

### **Neural Network Architecture**

```bibtex
@book{goodfellow2016deep,
  title={Deep learning},
  author={Goodfellow, Ian and Bengio, Yoshua and Courville, Aaron},
  year={2016},
  publisher={MIT press}
}
```

### **Physics-Informed Machine Learning**

```bibtex
@article{karniadakis2021physics,
  title={Physics-informed machine learning},
  author={Karniadakis, George Em and Kevrekidis, Ioannis G and Lu, Lu and Perdikaris, Paris and Wang, Sifan and Yang, Liu},
  journal={Nature Reviews Physics},
  volume={3},
  number={6},
  pages={422--440},
  year={2021},
  publisher={Nature Publishing Group}
}
```

```bibtex
@article{raissi2019physics,
  title={Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations},
  author={Raissi, Maziar and Perdikaris, Paris and Karniadakis, George Em},
  journal={Journal of Computational physics},
  volume={378},
  pages={686--707},
  year={2019},
  publisher={Elsevier}
}
```

## 📊 Data Science and Visualization

### **Scientific Computing Libraries**

```bibtex
@article{harris2020array,
  title={Array programming with NumPy},
  author={Harris, Charles R and Millman, K Jarrod and Van Der Walt, St{\'e}fan J and others},
  journal={Nature},
  volume={585},
  number={7825},
  pages={357--362},
  year={2020},
  publisher={Nature Publishing Group}
}
```

```bibtex
@software{mckinney2010data,
  title={Data structures for statistical computing in python},
  author={McKinney, Wes and others},
  booktitle={Proceedings of the 9th Python in Science Conference},
  volume={445},
  pages={51--56},
  year={2010}
}
```

```bibtex
@article{pedregosa2011scikit,
  title={Scikit-learn: Machine learning in Python},
  author={Pedregosa, Fabian and Varoquaux, Ga{\"e}l and Gramfort, Alexandre and others},
  journal={Journal of machine learning research},
  volume={12},
  number={Oct},
  pages={2825--2830},
  year={2011}
}
```

## 🎨 Visualization and Plotting

```bibtex
@article{hunter2007matplotlib,
  title={Matplotlib: A 2D graphics environment},
  author={Hunter, John D},
  journal={Computing in science \& engineering},
  volume={9},
  number={3},
  pages={90--95},
  year={2007},
  publisher={IEEE Computer Society}
}
```

```bibtex
@software{waskom2021seaborn,
  title={seaborn: statistical data visualization},
  author={Waskom, Michael L},
  journal={Journal of Open Source Software},
  volume={6},
  number={60},
  pages={3021},
  year={2021}
}
```

## 🏗️ Software Engineering and Development

### **Version Control and Collaboration**

```bibtex
@misc{github2025,
  title={GitHub: The world's leading software development platform},
  author={{GitHub Inc.}},
  year={2025},
  url={https://github.com}
}
```

### **Python Programming Language**

```bibtex
@misc{python2025,
  title={Python Programming Language},
  author={Python Software Foundation},
  year={2025},
  url={https://www.python.org}
}
```

## 📖 How to Cite This Work

If you use this project in your research or work, please cite it as:

```bibtex
@software{drag_coefficient_prediction_2025,
  title={Physics-Guided Neural Network for Drag Coefficient Prediction},
  author={Claude AI and Contributors},
  year={2025},
  url={https://github.com/Sakeeb91/drag-coefficient-prediction},
  note={Physics-guided neural network implementation for predicting drag coefficients of spheres in fluid flow}
}
```

## 🔗 Related Work and Extensions

For readers interested in extending this work, we recommend exploring:

1. **Physics-Informed Neural Networks (PiNNs)** for solving the Navier-Stokes equations directly
2. **Neural Ordinary Differential Equations (NODEs)** for dynamic fluid systems
3. **Multi-physics problems** involving heat transfer and mass transfer
4. **Uncertainty quantification** in physics-guided predictions
5. **Real-time applications** in computational fluid dynamics

## 📧 Contact for Academic Collaboration

For academic collaborations, research questions, or citation clarifications, please open an issue on the GitHub repository.

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**Note**: This project is designed for educational and research purposes. All references are provided for academic integrity and to guide further learning in physics-guided machine learning.