Towards probabilistic Weather Forecasting with Conditioned Spatio-Temporal Normalizing Flows

Generative normalizing flows are able to model multimodal spatial distributions, and they have been shown to model temporal correlations successfully as well. These models provide several benefits over other types of generative models due to their training stability, invertibility and efficiency in sampling and inference. This makes them a suitable candidate for stochastic spatio-temporal prediction problems, which are omnipresent in many fields of sciences, such as earth sciences, astrophysics or molecular sciences. In this paper, we present conditional normalizing flows for stochastic spatio-temporal modelling. The method is evaluated on the task of daily temperature and hourly geopotential map prediction from ERA5 datasets. Experiments show that our method is able to capture spatio-temporal correlations and extrapolates well beyond the time horizon used during training.

Learning Likelihoods with Conditional Normalizing Flows

Normalizing Flows (NFs) are able to model complicated distributions p(y) with strong inter-dimensional correlations and high multimodality by transforming a simple base density p(z) through an invertible neural network under the change of variables formula. Such behavior is desirable in multivariate structured prediction tasks, where handcrafted per-pixel loss-based methods inadequately capture strong correlations between output dimensions. We present a study of conditional normalizing flows (CNFs), a class of NFs where the base density to output space mapping is conditioned on an input x, to model conditional densities p(y|x). CNFs are efficient in sampling and inference, they can be trained with a likelihood-based objective, and CNFs, being generative flows, do not suffer from mode collapse or training instabilities. We provide an effective method to train continuous CNFs for binary problems and in particular, we apply these CNFs to super-resolution and vessel segmentation tasks demonstrating competitive performance on standard benchmark datasets in terms of likelihood and conventional metrics.