GCR Spectra Reconstructed with Neutron Monitor Yield Function and Artificial Neural Networks: Comparison of Two Methods

We present a framework that reconstructs time-resolved galactic cosmic-ray (GCR) proton and helium energy spectra from the global neutron monitor network, providing data about GCR flux without direct satellite observations. Two methods are utilized and compared: a calibrated yield function plus force-field scheme and artificial neural networks trained on multi-station neutron monitor count rates coupled with heliophysical indices. The reconstructed spectral time series reproduce both large-scale solar-cycle modulation and short-term disturbances and extend to periods lacking daily spacecraft data, including 2006–2011 (consistent with PAMELA) and 2019–2022 (consistent with AMS-02 Bartels rotation averages). Artificial neural networks deliver excellent performance across energies, with markedly lower mean absolute percentage error and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mi>χ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mi>/</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">d</mml:mi> <mml:mi mathvariant="normal">o</mml:mi> <mml:mi mathvariant="normal">f</mml:mi> </mml:mrow> </mml:mrow> </mml:math> near unity. A thorough validation confirms robustness and establishes neutron monitors as an effective real-time GCR spectrometer that can be utilized for various purposes.