Deep-ensemble modelling of electron flux at the radiation belt’s outer boundary with Bayesian neural networks (work in progress)

Motivations

The outer boundary condition in radiation belt models is often reconstructed from data. However, data availability is biased towards particular spacecraft orbits about the Earth (namely geosynchronous or geostationary orbits).

If the outer boundary is beyond these orbits (as T. Bloch et al., 2021, found), then radiation belt processes may not be properly accounted for in modelling

We aim to provide a synthetic dataset representing flux measurements at the outer boundary location identified in T. Bloch et al. (2021), for use in the future construction of the outer boundary condition.

Additionally, we see the obvious benefits of producing probabilistic outputs. Not only do these simply provide more information, they serve to improve down-stream data-assimilation using our results.

Methods

We train an ensemble of neural networks (BNN) to predict the 11 THEMIS SST fluxes (and uncertainty) at the outer boundary location using GOES and geomagnetic indices or solar wind data from OMNI.

Each of our NNs outputs 11 flux predictions and 11 variances (representing the aleatoric uncertainty). The variances are constrained by optimising the negative log-likelihood.

Our ensemble is constructed by training each member on bootstrapped data, with randomly sampled weights from a uniform prior, and optimised stochastically. As such, each trained member has different weights. These weights correspond to samples of the posterior distribution of the weights given the network and training data. The ensemble allows us to estimate the epistemic uncertainty.