Geometric Learning

EIT on symmetric domains has symmetric data: rotating the conductivity rotates the measurements. Networks that respect these symmetries need fewer parameters and less data. And EIT domains are rarely rectangles: networks for EIT must cope with arbitrary shapes, meshes and uneven resolution.

Reading order.

1. The symmetries: Symmetries of the EIT Problem, with the Dihedral Group D4 of the square as example.
2. Invariance and equivariance: Invariant and Equivariant Functions, Reynolds Operator.
3. Architectures: Invariant Filter Banks, Equivariant Convolutions.
4. Networks for EIT domains: Networks on EIT Domains, with Masked and Partial Convolutions, Conformal Transplantation of Networks and Graph Convolutions on Finite Element Meshes.

Related. Where these networks are used: Learned Priors; rotational symmetry is also what makes the disk solver fast (see Fast Solvers on Disk Domains).

References

1. M. M. Bronstein, J. Bruna, T. Cohen, P. Veličković (2021). Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges. arXiv:2104.13478