Various space missions have measured the total solar irradiance (TSI) since 1978. Among them the experiments Precision Monitoring of Solar Variability (PREMOS) on the PICARD satellite (2010–2014) and the Variability of Irradiance and Gravity Oscillations (VIRGO) on the mission Solar and Heliospheric Observatory, which started in 1996 and is still operational. Like most TSI experiments, they employ a dual-channel approach with different exposure rates to track and correct the inevitable degradation of their radiometers. Until now, the process of degradation correction has been mostly a manual process based on assumed knowledge of the sensor hardware. Here we present a new data-driven process to assess and correct instrument degradation using a machine-learning and data fusion algorithm, that does not require deep knowledge of the sensor hardware. We apply the algorithm to the TSI records of PREMOS and VIRGO and compare the results to the previously published results. The data fusion part of the algorithm can also be used to combine data from different instruments and missions into a composite time series. Based on the fusion of the degradation-corrected VIRGO/PMO6 and VIRGO/DIARAD time series, we find no significant change (i.e $$-0.17\pm 0.29$$ - 0.17 ± 0.29 W/m$$^2$$ 2 ) between the TSI levels during the two most recent solar minima in 2008/09 and 2019/20. The new algorithm can be applied to any TSI experiment that employs a multi-channel philosophy for degradation tracking. It does not require deep technical knowledge of the individual radiometers.
Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the adjoint method, many downstream tasks such as active learning, exploration in reinforcement learning, robust control, or filtering require accurate estimates of predictive uncertainties. In this work, we propose a novel approach towards estimating epistemically uncertain neural ODEs, avoiding the numerical integration bottleneck. Instead of modeling uncertainty in the ODE parameters, we directly model uncertainties in the state space. Our algorithm -distributional gradient matching (DGM) -jointly trains a smoother and a dynamics model and matches their gradients via minimizing a Wasserstein loss. Our experiments show that, compared to traditional approximate inference methods based on numerical integration, our approach is faster to train, faster at predicting previously unseen trajectories, and in the context of neural ODEs, significantly more accurate.
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