  The aim of this white paper is to briefly summarize some of the outstanding
gaps in the observations and modeling of stellar flares, CMEs, and exoplanetary
space weather, and to discuss how the theoretical and computational tools and
methods that have been developed in heliophysics can play a critical role in
meeting these challenges. The maturity of data-inspired and data-constrained
modeling of the Sun-to-Earth space weather chain provides a natural starting
point for the development of new, multidisciplinary research and applications
to other stars and their exoplanetary systems. Here we present recommendations
for future solar CME research to further advance stellar flare and CME studies.
These recommendations will require institutional and funding agency support for
both fundamental research (e.g. theoretical considerations and idealized
eruptive flare/CME numerical modeling) and applied research (e.g. data
inspired/constrained modeling and estimating exoplanetary space weather
impacts). In short, we recommend continued and expanded support for: (1.)
Theoretical and numerical studies of CME initiation and low coronal evolution,
including confinement of "failed" eruptions; (2.) Systematic analyses of
Sun-as-a-star observations to develop and improve stellar CME detection
techniques and alternatives; (3.) Improvements in data-inspired and
data-constrained MHD modeling of solar CMEs and their application to stellar
systems; and (4.) Encouraging comprehensive solar--stellar research
collaborations and conferences through new interdisciplinary and
multi-agency/division funding mechanisms.
