NCDL: A Framework for Deep Learning on non-Cartesian Lattices

• Project Github Page
• NCDL Documentation

The use of non-Cartesian grids is a niche but important topic in sub-fields of the numerical sciences, such as simulation and scientific visualization. However, nonCartesian approaches are virtually unexplored in machine learning. This is likely due to the difficulties in the representation of data on non-Cartesian domains and the lack of support for standard machine learning operations on non-Cartesian data. This paper proposes a new data structure called the lattice tensor which generalizes traditional tensor spatio-temporal operations to lattice tensors, enabling the use of standard machine learning algorithms on non-Cartesian data. We introduce a software library that implements this new data structure and demonstrate its effectiveness on various problems. Our method provides a general framework for machine learning on non-Cartesian domains, addressing the challenges mentioned above and filling a gap in the current literature.