Universal Physics Transformers
Benedikt Alkin Andreas Fürst Simon Schmid Lukas Gruber Markus Holzleitner Johannes Brandstetter
Deep neural network based surrogates for partial differential equations have
recently gained increased interest. However, akin to their numerical
counterparts, different techniques are used across applications, even if the
underlying dynamics of the systems are similar. A prominent example is the
Lagrangian and Eulerian specification in computational fluid dynamics, posing a
challenge for neural networks to effectively model particle- as opposed to
grid-based dynamics. We introduce Universal Physics Transformers (UPTs), a
novel learning paradigm which models a wide range of spatio-temporal problems -
both for Lagrangian and Eulerian discretization schemes. UPTs operate without
grid- or particle-based latent structures, enabling flexibility across meshes
and particles. UPTs efficiently propagate dynamics in the latent space,
emphasized by inverse encoding and decoding techniques. Finally, UPTs allow for
queries of the latent space representation at any point in space-time. We
demonstrate the efficacy of UPTs in mesh-based fluid simulations, steady-state
Reynolds averaged Navier-Stokes simulations, and Lagrangian-based dynamics.
Project page: https://ml-jku.github.io/UPT