Surface and volume fields

Predict the field everywhere in the domain, not just on the walls: velocity, pressure, temperature in the volume.

Surface quantities give the loads; volume quantities such as velocity, pressure and temperature explain them. Volume prediction uses query decoders, separate surface and volume branches and physics-consistent outputs.

Physical fields: Decide which quantities the model must reproduce before choosing the model.
Decoders: Turn latent tokens into surface pressure, shear or volume flow, with physics built into the output.
Cross-attention: A small set of queries reads from a large set of points, so cost stays linear.

Surface and volume fields

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