Benjamin Sanderse, researcher at CWI, Amsterdam.
Title: Energy-Consistent Generative Models for Fluid Flow Simulation
Abstract: Despite the enormous potential of generative modelling, its application to replace expensive physics simulations is still limited. One outstanding challenge in achieving efficient inference is to maintain physical consistency of the generated results. In this work, we address this challenge by leveraging the so-called stochastic interpolant framework [1] as a generative model, and incorporating energy consistency to enforce physical realism.
First, in the stochastic interpolant framework, one learns a stochastic differential equation (SDE) that maps samples from one distribution to another by defining a stochastic interpolation between the two distributions, which is then used to train a drift term in the SDE. In contrast to the widely used denoising diffusion probabilistic models, which are limited to Gaussian priors, the stochastic interpolant framework can map samples between arbitrary distributions. This is a crucial aspect, as in physics simulations (such as fluid flows), it allows us to perform time stepping from one distribution to the next without resorting to Gaussians. By applying this approach autoregressively, we can generate complete trajectories, while accounting for the inherent uncertainty by producing multiple plausible outcomes from the same initial condition.
Second, the incorporation of energy consistency, see e.g. [2], ensures that the generated trajectories adhere to the laws of physics. We demonstrate the effectiveness of our method with examples from incompressible fluid dynamics.
[1] M. S. Albergo, N. M. Boffi, E. Vanden-Eijnden, Stochastic interpolants: A unifying framework for flows and diffusions, arXiv preprint arXiv:2303.08797 (2023).
[2] T. van Gastelen, W. Edeling, B. Sanderse, Energy-conserving neural network for turbulence closure modeling, Journal of Computational Physics 508, 113003.
