The source code for our turbulent flow simulations using Autoregressive Conditional Diffusion Models (ACDMs) is online now at https://github.com/tum-pbs/autoreg-pde-diffusion , let us know how it works!
Project summary: Our work targets the prediction of turbulent flow fields from an initial condition using autoregressive conditional diffusion models (ACDMs). Our method relies on the DDPM approach, a class of generative models based on a parameterized Markov chain. They can be trained to learn the conditional distribution of a target variable given a conditioning. In our case, the target variable is the flow field at the next time step, and the conditioning is the flow field at the current time step, i.e., the simulation trajectory is created via autoregressive unrolling of the model. We showed that ACDMs can accurately and probabilistically predict turbulent flow fields, and that the resulting trajectories align with the statistics of the underlying physics. Furthermore, ACDMs can generalize to flow parameters beyond the training regime, and exhibit high temporal rollout stability, without compromising the quality of generated samples.
More details can also be found on the project website.
