Fengbo is a deep learning pipeline built entirely in Clifford Algebra to solve 3D Partial Differential Equations (PDEs), specifically for Computational Fluid Dynamics (CFD). It leverages 3D Convolutional and Fourier Neural Operator (FNO) layers, making it a powerful, physics-aware, and interpretable approach to PDE modeling.
✅ Clifford Algebra-Based: Works entirely in 3D Clifford Algebra for enhanced geometric and physics-based understanding.
✅ Efficient Architecture: Uses only 42 million trainable parameters with a streamlined design.
✅ Superior Accuracy: Outperforms 5 out of 6 models reported in Li et al. 2024 on the ShapeNet Car dataset.
✅ Computationally Efficient: Reduces complexity compared to graph-based methods.
✅ Interpretable Outputs: Outputs can be visualized as 3D physical quantities, making it a white-box model.
✅ Joint Estimation: Simultaneously predicts pressure and velocity fields.
Fengbo models PDE solutions as an interpretable mapping from geometry to physics, ensuring an efficient, geometry-aware, and physics-consistent solution. It consists of:
- 3D Convolutional Layers 🧩
- Fourier Neural Operator (FNO) Layers 🎛️
- Clifford Algebra Operations 📐
This combination allows for a direct mapping from input geometries to the corresponding physics fields, achieving both efficiency and accuracy.
To install and set up Fengbo, follow these steps:
# Clone the repository
git clone https://github.com/albertomariapepe/Fengbo.git
pip install -r requirements.txtIf you use Fengbo in your research, please cite:
@inproceedings{pepefengbo,
title={Fengbo: a Clifford Neural Operator pipeline for 3D PDEs in Computational Fluid Dynamics},
author={Pepe, Alberto and Montanari, Mattia and Lasenby, Joan},
booktitle={The Thirteenth International Conference on Learning Representations}
}
We welcome contributions! Feel free to open issues or submit PRs.
For any inquiries, reach out via email or open an issue on GitHub.