Architecture / Building blocks

Decoders

Turn latent tokens into surface pressure, shear or volume flow, with physics built into the output.

The decoder turns latent tokens into numbers engineers use: surface pressure, wall shear, velocity in the volume. Its design decides accuracy where it matters.

• Neural-field decoders evaluate any coordinate, so surface and volume fields can come from the same latent state.
• Anchors (AB-UPT): a subset of anchor points carries the expensive attention; the remaining millions of query points attend only to the anchors.
• Separate branches for geometry, surface and volume decouple tasks that need different resolution.
• Physics consistency can be built in, for example a divergence-free velocity formulation, instead of hoping the network learns it.
• Generative decoders (diffusion, flow matching) model uncertainty and stay stable over long rollouts.

Industrial example: A model that cannot lose mass

In a duct, whatever flows in must flow out: narrow the section and the flow must speed up. A divergence-free decoder builds this rule into the architecture, so every prediction conserves mass, just like a trusted solver.

References

• AB-UPT: Anchored-Branched Universal Physics Transformers (Emmi AI, TMLR 2025)
• AROMA: Latent PDE Modeling with Local Neural Fields (Serrano et al., NeurIPS 2024)
• Universal Physics Transformers (Alkin et al., NeurIPS 2024)

Related

• Cross-attention: A small set of queries reads from a large set of points, so cost stays linear.
• Surface and volume fields: Predict the field everywhere in the domain, not just on the walls: velocity, pressure, temperature in the volume.
• Latent space: Compress millions of points into a few hundred learned slots that hold the physics.