\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[english]{babel}



\usepackage{float}








\begin{document}

\title{Probabilistic Short-Term Solar Driver Forecasting with Neural Network
Ensembles}



\author[1]{Joshua D Daniell}%
\author[1]{Piyush M Mehta}%
\affil[1]{West Virginia University}%


\vspace{-1em}



  
  \date{May 25, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Space weather indices are used to drive forecasts of thermosphere
density, which directly affects objects in low-Earth orbit (LEO) through
atmospheric drag force. A set of proxies and indices (drivers),
F\textsubscript{10.7}, S\textsubscript{10.7}, M\textsubscript{10.7}, and
Y\textsubscript{10.7} are used as inputs by the JB2008 thermosphere
density model. The United States Air Force (USAF) operational High
Accuracy Satellite Drag Model (HASDM), relies on JB2008, and forecasts
of solar drivers from a linear algorithm. We introduce methods using
long-short term memory (LSTM) model ensembles to improve over the
current prediction method as well as a previous univariate approach. We
investigate the usage of principal component analysis (PCA) to enhance
multivariate forecasting. A novel method, referred to as striped
sampling, is created to produce statistically consistent machine
learning data sets. We also investigate forecasting performance and
uncertainty estimation by varying the training loss function and by
investigating novel weighting methods. Results show that stacked neural
network model ensembles make multivariate driver forecasts which
outperform the operational linear method. When using MV-MLE
(multivariate multi-lookback ensemble), we see an improvement of RMSE
for F\textsubscript{10.7}, S\textsubscript{10.7}, M\textsubscript{10.7},
and Y\textsubscript{10.7} of 17.7\%, 12.3\%, 13.8\%, 13.7\%
respectively, over the operational method. We provide the first
probabilistic forecasting method for S\textsubscript{10.7},
M\textsubscript{10.7}, and Y\textsubscript{10.7} . Ensemble approaches
are leveraged to provide a distribution of predicted values, allowing an
investigation into robustness and reliability (R\&R) of uncertainty
estimates. Uncertainty was also investigated through the use of
calibration error score (CES), with the approach providing an average
CES of 5.63\%, across all drivers.%
\end{abstract}%



\sloppy




\selectlanguage{english}
\FloatBarrier
\end{document}

