Probabilistic predictions with Fourier neural operators

Neural networks have been successfully applied in modeling partial differential equations, especially in dynamical systems. Commonly used models, such as neural operators, are performing well at deterministic prediction tasks, but lack a quantification of the uncertainty inherent in many complex systems, for example weather forecasting. In this paper, we explore a new approach that combines Fourier neural operators with generative modeling based on proper scoring rules in order to create well-calibrated probabilistic predictions of dynamical systems. We demonstrate improved predictive uncertainty for our approach, especially in settings with very high inherent uncertainty.