Geometric Clifford Algebra Networks and Clifford Neural Layers for PDE Modeling

Explore the applications of Geometric Clifford Algebra Networks and Clifford Neural Layers in PDE modeling through this comprehensive conference talk. Delve into the fundamentals of Clifford algebras and their relevance to deep learning, covering topics such as Clifford convolution, Clifford Fourier transforms, and group action layers. Discover how these advanced mathematical concepts can be applied to improve neural PDE surrogates, particularly in fluid dynamics and weather modeling. Learn from expert speaker Johannes Brandstetter as he discusses two groundbreaking papers on the subject, providing insights into the theoretical advantages and practical implementations of these novel approaches. Gain a deeper understanding of how multivector representations and Clifford algebraic operations can enhance the modeling of physical systems and potentially revolutionize fields such as fluid dynamics and weather forecasting.

- Intro
- Why Clifford Algebras for Deep Learning
- Introduction to Clifford Algebras
- Clifford Convolution
- Clifford Fourier Transform & Results
- Follow Up Work
- Geometric Clifford Algebra Networks
- The Pinn Group and Transformations
- The Overall Picture
- Group Action Layers
- Fluid Dynamics
- Q+A