Cluster Attention Neural Operators for Solving Parametric Partial Differential Equations
This study addresses the computational redundancy of traditional PDE simulations, the high complexity of Transformer attention, and the information loss inherent in spatial projections by proposing the CANO model. Its core innovation lies in introducing dynamic query clustering under a cross-attention mechanism while preserving full-resolution key-value mappings. This design circumvents the losses associated with patch-based compression and the constraints of weight sharing, thereby enabling efficient, lossless capture of global dependencies. Experimental evaluations demonstrate that CANO achieves state-of-the-art accuracy across fluid dynamics, solid mechanics, and irregular geometry benchmarks, exhibiting superior geometric adaptability and temporal consistency.