Bayesian Parameter Estimation in Geospace Modeling (Invited Presentation)

Ensemble modeling is rapidly becoming an important and widespread methodology in space weather forecasting, following an established trend in meteorological weather. Often, ensemble modeling can be used to increase the prediction accuracy of a model, but it is also a straightforward way of estimating error bars and propagating uncertainties from model inputs to the quantities of interest.

However, an often-overlooked aspect of the uncertainty quantification within ensemble modeling is that such a method works only when the uncertainty associated with each input has been accurately estimated. In other words, an ensemble simulation that propagates uncertainties that are not realistic, or improperly calibrated, will return a meaningless result. The main difficulty in assigning uncertainties to inputs is that generally such inputs are not directly observed, but only estimated.

One of the most robust statistical method of estimating parameters and their distribution is to use a Bayesian approach, such as a Markov Chain Monte-Carlo (MCMC) approach. MCMC is very expensive (even more than the ensemble run), and thus strategies involving machine learning have been developed to alleviate its computational cost.

In this talk we present an overview of MCMC approaches in Space Weather and provide an example application in Geospace modeling. In particular, we emphasize the use of a physics-informed neural network for parameter estimation in order to develop probabilistic forecasts to better assist space weather forecasters and customers in understanding model prediction uncertainty and in responding to potential space weather threats.