Geometric Algebra/Machine Learning Project

MANAGER: Tyler Hadsell

CONTACT: Thadsell@g.ucla.edu

Learning Objectives: Compare with classic vector algebra to understand advantages/disadvantages. Understand new concepts: “multi-vectors”, “wedge-products”, and “geometric-product”. Analyze applications and comparisons in linear algebra. Implement geometric algebra in the study of classical mechanics.

Prerequisites: Multivariable Calculus, Slight understanding of Linear Algebra. Physics 1A&1B. Python or some other basic programming knowledge. Willingness and excitement to learn!!

Machine Learning Objectives:

Learning python-based machine learning libraries (PyTorch, TensorFlow, Scikit-learn.

Learn python based data visualization methods (Paraview) to analyze trends.

Implement Classical Mechanics conservation laws, partial differential equations
and other system governing mathematics into machine learning algorithms and
utilize Physics Informed Neural Networks (PINNs).

Compare Classical Mechanics laws written in geometric algebra and classical
vector algebra and their implications when fed into PINNs.