Welcome to SymDet’s documentation!¶
SymDet is a python package developed in conjunction with PhD research into extraction of fundamental physical laws from raw data. Specifically, SymDet provides the functionality for performing the analysis described in the paper by Sven Krippendorf and Marc Syvaeri on Detecting symmetries with neural networks.
The main idea behind this method is twofold.
1. The embedding layer of a neural network holds within it an encoded representation from which symmetries in data can be studied.
2. By formulating the problem as regression, one can extract the generators of the Lie algebra from the point clouds generated in this representation.
At the moment the code can perform the following tasks.
Use a dense neural network to construct a tSNE representation to visually identify symmetry groups.
Fit generators of symmetry groups using given point cloud data. I can only confirm the accuracy of this fitting for two dimensional data but am working to extend this to arbitrary systems.
Identify groups connected by symmetry in the tSNE representation and collect them for generator extraction.
First Steps:
Theoretical Minimum: