Architecture

The building blocks of modern field surrogates, how they scale, and the model families built from them.

• Tokens: Each mesh point becomes a vector of numbers describing where it is and what it carries.
• Latent space: Compress millions of points into a few hundred learned slots that hold the physics.
• Self-attention: Every token looks at every other token and decides what matters to it.
• Cross-attention: A small set of queries reads from a large set of points, so cost stays linear.
• Decoders: Turn latent tokens into surface pressure, shear or volume flow, with physics built into the output.
• Scaling to millions of points: Attention grows with the square of the points; latent and linear schemes keep it tractable.
• JEPA: Predict the latent of the flow from geometry and condition; decode a field only when you need one.
• Model families: Neural fields, U-Nets, graph networks and transformers, and what each is good for.