Probabilistic Super-Resolution of Solar Magnetograms: Generating Many Explanations and Measuring Uncertainties

Machine learning techniques have been successfully applied to super-resolution tasks on natural images where visually pleasing results are sufficient. However in many scientific domains this is not adequate and estimations of errors and uncertainties are crucial. To address this issue we propose a Bayesian framework that decomposes uncertainties into epistemic and aleatoric uncertainties. We test the validity of our approach by super-resolving images of the Sun's magnetic field and by generating maps measuring the range of possible high resolution explanations compatible with a given low resolution magnetogram

Single-Frame Super-Resolution of Solar Magnetograms: Investigating Physics-Based Metrics \& Losses

Breakthroughs in our understanding of physical phenomena have traditionally followed improvements in instrumentation. Studies of the magnetic field of the Sun, and its influence on the solar dynamo and space weather events, have benefited from improvements in resolution and measurement frequency of new instruments. However, in order to fully understand the solar cycle, high-quality data across time-scales longer than the typical lifespan of a solar instrument are required. At the moment, discrepancies between measurement surveys prevent the combined use of all available data. In this work, we show that machine learning can help bridge the gap between measurement surveys by learning to \textbf{super-resolve} low-resolution magnetic field images and \textbf{translate} between characteristics of contemporary instruments in orbit. We also introduce the notion of physics-based metrics and losses for super-resolution to preserve underlying physics and constrain the solution space of possible super-resolution outputs

Dropout inference in Bayesian neural networks with alpha-divergences

To obtain uncertainty estimates with real-world Bayesian deep learning models, practical inference approximations are needed. Dropout variational inference (VI) for example has been used for machine vision and medical applications, but VI can severely underestimates model uncertainty. Alpha-divergences are alternative divergences to VI’s KL objective, which are able to avoid VI’s uncertainty underestimation. But these are hard to use in practice: existing techniques can only use Gaussian approximating distributions, and require existing models to be changed radically, thus are of limited use for practitioners. We propose a re-parametrisation of the alpha-divergence objectives, deriving a simple inference technique which, together with dropout, can be easily implemented with existing models by simply changing the loss of the model. We demonstrate improved uncertainty estimates and accuracy compared to VI in dropout networks. We study our model’s epistemic uncertainty far away from the data using adversarial images, showing that these can be distinguished from non-adversarial images by examining our model’s uncertainty

Physically motivated deep learning to superresolve and cross calibrate solar magnetograms

Superresolution (SR) aims to increase the resolution of images by recovering detail. Compared to standard interpolation, deep learning-based approaches learn features and their relationships to leverage prior knowledge of what low-resolution patterns look like in higher resolution. Deep neural networks can also perform image cross-calibration by learning the systematic properties of the target images. While SR for natural images aims to create perceptually convincing results, SR of scientific data requires careful quantitative evaluation. In this work, we demonstrate that deep learning can increase the resolution and calibrate solar imagers belonging to different instrumental generations. We convert solar magnetic field images taken by the Michelson Doppler Imager (resolution ∼2″ pixel−1; space based) and the Global Oscillation Network Group (resolution ∼2.″5 pixel−1; ground based) to the characteristics of the Helioseismic and Magnetic Imager (resolution ∼0.″5 pixel−1; space based). We also establish a set of performance measurements to benchmark deep-learning-based SR and calibration for scientific applications