Physics-Based Reconstruction of CME-driven SEPs: Optimization via Multi-Spacecraft Observations

Accurate prediction of Solar Energetic Particle (SEP) events is critical for mitigating space weather risks, yet current forecasting models face significant uncertainties in determining physical parameters. This challenge extends beyond our solar system; recent detections of stellar Type II radio bursts (e.g., Callingham et al. 2025) imply shock-driven particle acceleration in exoplanetary systems, but quantifying their habitability impact requires validated acceleration and transport models. Since direct observation is impossible, stellar space weather models must rely on SEP simulations grounded in solar physics. The challenge is that key physical parameters (e.g., injection efficiency $\epsilon$, mean free path $\lambda$) are often degenerate and difficult to constrain even in solar events. 
We present a framework to rigorously determine these parameters using the Sun as a laboratory. We employ a physics-based model coupled with mathematical optimization. We combined a CME propagation model (SUSANOO, SUSANOO-CME; Shiota et al., 2014, 2016) with an acceleration and transport model with the diffusive shock acceleration and the focused transport equation (Minoshima et al., in review), and applied it to the major SEP event of 9 October 2021. To explore the high-dimensional parameter space efficiently and robustly, we introduced optimization methods such as the evolution strategy. Our framework successfully reproduced proton fluxes simultaneously across five spatially distributed spacecraft. A crucial finding is the necessity of spatial refinement: treating injection efficiency and transport parameters independently for each longitudinal bin improves physical consistency compared to uniform assumptions. Our analysis reveals that the injection efficiency is the dominant factor governing the flux. This study not only advances solar SEP forecasting but also provides a validated, physics-based baseline for modeling radiation environments in active cool star systems.