4 papers
Computing statistical Euler limits of the Navier--Stokes equations in three dimensions
Johannes L. Grafen, Tobias Rohner, Stephan Simonis
We develop a Monte Carlo lattice Boltzmann method to compute statistical solutions to the three-dimensional incompressible Navier--Stokes and Euler equations. Entropic space-time a…
Sufficient Conditions for the Energy Balance for the Stochastic Incompressible Euler Equations with Additive Noise in two Space Dimensions
Tobias Rohner, Franziska Weber
We consider vanishing viscosity approximations to solutions of the stochastic incompressible Euler equations in two space dimensions with additive noise. We identify sufficient and…
Generative AI for fast and accurate statistical computation of fluids
Roberto Molinaro, Samuel Lanthaler, Bogdan Raonić +9
We present a generative AI algorithm for addressing the pressing task of fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. Our algorith…
Poseidon: Efficient Foundation Models for PDEs
Maximilian Herde, Bogdan Raonić, Tobias Rohner +4
We introduce Poseidon, a foundation model for learning the solution operators of PDEs. It is based on a multiscale operator transformer, with time-conditioned layer norms that enab…