Prediction of isotropic turbulence using conditional diffusion probabilistic models*

Recent advances in deep learning (DL) have centered around generative models. These models learn unknown data distributions to generate new samples from noise. However, they can be extended to enable a wide range of applications by incorporating conditional inputs. In turbulence problems, dynamics prediction that uses fields from previous time steps to predict future states is a representative application. Although GAN-based models have dominated the field, challenges remain, such as scalability and training instability. Diffusion probabilistic models (DMs), which have recently gained attention, offer the flexibility of likelihood-based models while achieving performance comparable to or surpassing that of GANs. Nevertheless, they require significantly higher computational costs, sometimes up to thousands of times greater than GAN-based models with similar performance.

In this presentation, we apply a DM to the problem of predicting 2D turbulence and conduct a comprehensive performance evaluation, comparing it against various DL models, including a conditional GAN, which has previously shown the highest performance. We found that our DM outperforms others for relatively short lead times. However, the DM suffers from severe performance degradation for longer lead times where the autocorrelation drops below 0.25, indicating low temporal stability. Additionally, we are exploring the extension of the DM to 3D turbulence prediction, which has been rarely reported.