Authors: N.V. Pogorelov (University of Alabama in Huntsville), C. N. Arge (NASA Goddard Space Flight Center), R. M. Caplan (Predictive Science), , P. C. Colella (Lawrence Berkeley National Laboratory), C. Gebhart (Lawrence Berkeley National Laboratory), D. V. Hegde (University of Alabama in Huntsville), S. Jones (NASA Goddard Space Flight Center), T. K. Kim (University of Alabama in Huntsville), J. A. Linker (Predictive Science), T. Newman (University of Alabama in Huntsville), T. Singh (Georgia State University), B. Van Straalen (Lawrence Berkeley National Laboratory), L. M. Upton (Southwest Research Institute), R. Attie (Predictive Science), S. Raza (university of Alabama in Huntsville), M. Stulajter (Predictive Science), J. Turtle (Predictive Science)

Successful space weather (SWx) forecasts require a synergy of data analysis, numerical simulations, and machine learning (ML). A traditional way to address the challenges in SWx physics is to derive the boundary conditions for coronal models using data assimilation on the photosphere and surface flux transport models, run coronal models to heliocentric distances outside of the Alfvénic surface, and use the obtained solutions in corresponding heliospheric models. Because of the uncertainties in the photospheric boundary conditions, ensemble modeling is inevitable for SWx forecasts. By analyzing time-dependent, data-driven simulations of the ambient solar wind at multiple space locations, we determine the associated uncertainties and quantify them. Coronal mass ejections (CMEs) are typically inserted into the ambient solar wind in the corona. This procedure is also characterized by uncertainties in the determination of CME properties from their remote observations. The major challenges in SWx forecasts are the correct determination of CME arrival at Earth (or other planets) and the magnetic field they carry. A plethora of ensemble simulations has demonstrated that uncertainties are not acceptable, being about 12 hours for CME arrival on the average. We present a new sequence of open-source SWx software based on the combination of the Open Flux Transport (OFT) model for assimilation of photospheric magnetograms and obtaining magnetic field distributions over the full surface of the Sun,  the Wang-Sheeley-Arge model of the solar corona, and HelioCubed, as a heliospheric model ensuring a genuinely fourth order of convergence both in space and time on cubed-sphere grids. The presented analysis shows that ML techniques can be used (1) to automatize the quantification of uncertainties in ensemble modeling and (2) improve the forecasts themselves. For example, a mismatch between the modeled and observed CME arrival can be decreased 2-3 times even if no ensemble performs acceptably. Once a successful forecast is made, it is possible to backtrack the reasons of errors introduced by multiple uncertainties and determine the sensitivity of forecasts to different sources of uncertainties. ML is also of importance for prediction of solar flare eruptions, the accuracy of which strongly depends on the history of their evolution.