Probabilistic neural operators for functional uncertainty quantification

Neural operators aim to approximate the solution operator of a system of differential equations purely from data. They have shown immense success in modeling complex dynamical systems across various domains. However, the occurrence of uncertainties inherent in both model and data has so far rarely been taken into account\textemdash{}a critical limitation in complex, chaotic systems such as weather forecasting. In this paper, we introduce the probabilistic neural operator (PNO), a framework for learning probability distributions over the output function space of neural operators. PNO extends neural operators with generative modeling based on strictly proper scoring rules, integrating uncertainty information directly into the training process. We provide a theoretical justification for the approach and demonstrate improved performance in quantifying uncertainty across different domains and with respect to different baselines. Furthermore, PNO requires minimal adjustment to existing architectures, shows improved performance for most probabilistic prediction tasks, and leads to well-calibrated predictive distributions and adequate uncertainty representations even for long dynamical trajectories. Implementing our approach into large-scale models for physical applications can lead to improvements in corresponding uncertainty quantification and extreme event identification, ultimately leading to a deeper understanding of the prediction of such surrogate models.

Estimation of spatio-temporal extremes via generative neural networks

Recent methods in modeling spatial extreme events have focused on utilizing parametric max-stable processes and their underlying dependence structure. In this work, we provide a unified approach for analyzing spatial extremes with little available data by estimating the distribution of model parameters or the spatial dependence directly. By employing recent developments in generative neural networks we predict a full sample-based distribution, allowing for direct assessment of uncertainty regarding model parameters or other parameter dependent functionals. We validate our method by fitting several simulated max-stable processes, showing a high accuracy of the approach, regarding parameter estimation, as well as uncertainty quantification. Additional robustness checks highlight the generalization and extrapolation capabilities of the model, while an application to precipitation extremes across Western Germany demonstrates the usability of our approach in real-world scenarios.

Uncertainty quantification for data-driven weather models

Artificial intelligence (AI)-based data-driven weather forecasting models have experienced rapid progress over the last years. Recent studies, with models trained on reanalysis data, achieve impressive results and demonstrate substantial improvements over state-of-the-art physics-based numerical weather prediction models across a range of variables and evaluation metrics. Beyond improved predictions, the main advantages of data-driven weather models are their substantially lower computational costs and the faster generation of forecasts, once a model has been trained. However, most efforts in data-driven weather forecasting have been limited to deterministic, point-valued predictions, making it impossible to quantify forecast uncertainties, which is crucial in research and for optimal decision making in applications. Our overarching aim is to systematically study and compare uncertainty quantification methods to generate probabilistic weather forecasts from a state-of-the-art deterministic data-driven weather model, Pangu-Weather. Specifically, we compare approaches for quantifying forecast uncertainty based on generating ensemble forecasts via perturbations to the initial conditions, with the use of statistical and machine learning methods for post-hoc uncertainty quantification. In a case study on medium-range forecasts of selected weather variables over Europe, the probabilistic forecasts obtained by using the Pangu-Weather model in concert with uncertainty quantification methods show promising results and provide improvements over ensemble forecasts from the physics-based ensemble weather model of the European Centre for Medium-Range Weather Forecasts for lead times of up to 5 days.