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About this paper
Edoardo Calvello, Nikola B. Kovachki, Matthew E. Levine, Andrew M. Stuart
The authors define Transformer Neural Operator (TNO) attention over continuous functions, with normalized query–key scores forming a domain probability density approximated by a discrete sum. On low-resolution 64×64 lognormal Darcy flow, TNO achieves median test relative L2 error 1.19×10⁻² versus FNO’s 1.96×10⁻², using 5.98×10⁵ versus 5.70×10⁶ parameters. Pointwise attention is quadratic in grid points, and errors can vary across resolutions.
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