Geometric Deep Learning for Molecular Modeling

 

  1. Introduction to group convolutional neural networks (G-CNNs):
  • Equivariance to translation
  • Generalized equivariance

 

  1. Symmetries and group representation theory
    • Groups and homogeneous spaces
    • Group representations
    • Integrating functions on groups

 

  1. Generalized harmonic analysis (Part I)
    • Fourier analysis on compact groups
    • The case of rotations: SO(3)
    • Convolution theorem on compact groups
    •  
  2. Generalized Harmonic analysis (Part II)
    • Representations of SO(3)
    • Fourier analysis on homogeneous spaces

 

  1. Equivariance to Euclidean group SE(3)
    • Steerable G-CNNs and tensor field networks

 

  1. Spherical CNNs
    • Correlation on the sphere and rotation group
    • Generalized Fast Fourier Transform

 

  1. Simpler implementations of equivariance
    • Equivariant graph neural network (EGNN)
    • Equivariant message passing for tensorial properties prediction

 

  1. Equivariance and self-attention
    • SE(3)-Transformer
    • Equivariant Transformer

 

  1. Applications of geometric deep learning for molecular systems
    • Quantum chemistry, molecular dynamics and drug discovery

 

  1. Geometrical modules in AlphaFold2
    • Pair representations and triangular updates
    • Invariant point attention (IPA)
    • Equivariant module

 

  1. Possible extra-topics:
  • Equivariant diffusion models and molecular generation
  • General theory of equivariant CNNs on homogeneous spaces