  Uncertainty quantification is crucial to decision-making. A prominent example
is probabilistic forecasting in numerical weather prediction. The dominant
approach to representing uncertainty in weather forecasting is to generate an
ensemble of forecasts. This is done by running many physics-based simulations
under different conditions, which is a computationally costly process. We
propose to amortize the computational cost by emulating these forecasts with
deep generative diffusion models learned from historical data. The learned
models are highly scalable with respect to high-performance computing
accelerators and can sample hundreds to tens of thousands of realistic weather
forecasts at low cost. When designed to emulate operational ensemble forecasts,
the generated ones are similar to physics-based ensembles in important
statistical properties and predictive skill. When designed to correct biases
present in the operational forecasting system, the generated ensembles show
improved probabilistic forecast metrics. They are more reliable and forecast
probabilities of extreme weather events more accurately. While this work
demonstrates the utility of the methodology by focusing on weather forecasting,
the generative artificial intelligence methodology can be extended for
uncertainty quantification in climate modeling, where we believe the generation
of very large ensembles of climate projections will play an increasingly
important role in climate risk assessment.
