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\begin{document}

\title{Reduced-Order Probabilistic Emulation of Physics-Based Ring Current
Models: Application to RAM-SCB Particle Flux}



\author[1]{Alfredo A Cruz}%
\author[1]{Piyush M Mehta}%
\author[2]{Steven K. Morley}%
\author[2]{Humberto C Godinez}%
\author[3]{Vania K. Jordanova}%
\affil[1]{West Virginia University}%
\affil[2]{Los Alamos National Laboratory (DOE)}%
\affil[3]{LANL}%


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  \date{May 24, 2024}


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\begin{abstract}
We present a proof of concept for the probabilistic emulation of the
Ring current-Atmosphere interactions Model with Self-Consistent magnetic
field (RAM-SCB) particle flux. We extend the workflow developed by
Licata and Mehta (2023) by applying it to the ring current and further
developing its uncertainty quantification methodology. We introduce a
novel approach for sampling over 20 years of solar and geomagnetic
activity to identify 30 simulation periods, each one week long, to
generate the training, validation, and test datasets. Large-scale
physics-based simulation models for the ring current can be
computationally expensive. This work aims at creating an emulator that
is more efficient, capable of forecasting, and provides an estimate on
the uncertainty of its predictions, all without requiring large
computational resources. We demonstrate the emulation process on a
subset of particle flux: a single energy channel of omnidirectional
flux. A principal component analysis (PCA) is used for the
dimensionality reduction into the reduced-space, and the dynamic
modeling is performed with a recurrent neural network. A hierarchical
ensemble of Long-Short Term Memory (LSTM) neural networks provides the
statistics needed to produce a probabilistic output, resulting in a
reduced-order probabilistic emulator (ROPE) that performs time-series
forecasting of the ring current's particle flux with an estimate on its
uncertainty distribution. The resulting ROPE from this smaller subset of
RAM-SCB particle flux provides dynamic predictions with errors less than
11\% and calibration scores under 10\%, demonstrating that this workflow
can provide a probabilistic emulator with a robust and reliable
uncertainty estimate when applied to the ring current.%
\end{abstract}%



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