CATO: Geometry-Adaptive Neural Operator for PDEs on Complex Domains

The Charted Axial Transformer Operator (CATO) has been developed by researchers as a neural operator aimed at addressing partial differential equations (PDEs) within intricate geometries. Unlike traditional transformer-based operators that directly handle extensive mesh points or utilize unrefined discretization coordinates, CATO creates a continuous latent chart that translates mesh coordinates into a learned chart space. This innovative space employs chart-conditioned axial attention to effectively manage long-range dependencies while minimizing computational costs. This method tackles significant challenges faced by current neural PDE solvers, especially the high computational demands associated with complex geometries and the obscuring effects of raw coordinate systems on intrinsic geometry. The findings were shared on arXiv with the identifier 2605.09016.