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 <front>
  <journal-meta>
   <journal-id journal-id-type="publisher-id">Solar-Terrestrial Physics</journal-id>
   <journal-title-group>
    <journal-title xml:lang="en">Solar-Terrestrial Physics</journal-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Solar-Terrestrial Physics</trans-title>
    </trans-title-group>
   </journal-title-group>
   <issn publication-format="online">2500-0535</issn>
  </journal-meta>
  <article-meta>
   <article-id pub-id-type="publisher-id">6a9c168032807fdbab8763a2</article-id>
   <article-id pub-id-type="doi">10.12737/stp-123202606</article-id>
   <article-id pub-id-type="edn">kuybhp</article-id>
   <article-categories>
    <subj-group subj-group-type="toc-heading" xml:lang="ru">
     <subject>Results of current research</subject>
    </subj-group>
    <subj-group subj-group-type="toc-heading" xml:lang="en">
     <subject>Results of current research</subject>
    </subj-group>
    <subj-group>
     <subject>Results of current research</subject>
    </subj-group>
   </article-categories>
   <title-group>
    <article-title xml:lang="en">Machine-learning method for reconstructing near-Earth low-energy cosmic ray fluxes from ground-based SOPO neutron monitor data</article-title>
    <trans-title-group xml:lang="ru">
     <trans-title>Machine-learning method for reconstructing near-Earth low-energy cosmic ray fluxes from ground-based SOPO neutron monitor data</trans-title>
    </trans-title-group>
   </title-group>
   <contrib-group content-type="authors">
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Лагойда</surname>
       <given-names>Илья Алексеевич</given-names>
      </name>
      <name xml:lang="en">
       <surname>Lagoida</surname>
       <given-names>Ilya Alekseevich</given-names>
      </name>
     </name-alternatives>
     <email>IALagoida@mephi.ru</email>
     <bio xml:lang="ru">
      <p>кандидат физико-математических наук;</p>
     </bio>
     <bio xml:lang="en">
      <p>candidate of physical and mathematical sciences;</p>
     </bio>
     <xref ref-type="aff" rid="aff-1"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Воронов</surname>
       <given-names>Сергей Александрович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Voronov</surname>
       <given-names>Sergei Aleksandrovich</given-names>
      </name>
     </name-alternatives>
     <email>sergvor@gmail.com</email>
     <xref ref-type="aff" rid="aff-2"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Барбашина</surname>
       <given-names>Наталья Сергеевна</given-names>
      </name>
      <name xml:lang="en">
       <surname>Barbashina</surname>
       <given-names>Natalia Sergeevna</given-names>
      </name>
     </name-alternatives>
     <email>NSBarbashina@mephi.ru</email>
     <xref ref-type="aff" rid="aff-3"/>
    </contrib>
    <contrib contrib-type="author">
     <name-alternatives>
      <name xml:lang="ru">
       <surname>Астапов</surname>
       <given-names>Иван Иванович</given-names>
      </name>
      <name xml:lang="en">
       <surname>Astapov</surname>
       <given-names>Ivan Ivanovich</given-names>
      </name>
     </name-alternatives>
     <email>IIastapov@mephi.ru</email>
     <xref ref-type="aff" rid="aff-4"/>
    </contrib>
   </contrib-group>
   <aff-alternatives id="aff-1">
    <aff>
     <institution xml:lang="ru">Национальный исследовательский ядерный университет «МИФИ»</institution>
     <city xml:lang="ru">Москва</city>
     <country country="RU" xml:lang="ru">Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">National Research Nuclear University MEPhI</institution>
     <city xml:lang="en">Moscow</city>
     <country country="RU" xml:lang="en">Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-2">
    <aff>
     <institution xml:lang="ru">Национальный исследовательский ядерный университет «МИФИ»</institution>
     <city xml:lang="ru">Москва</city>
     <country country="RU" xml:lang="ru">Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">National Research Nuclear University MEPhI</institution>
     <city xml:lang="en">Moscow</city>
     <country country="RU" xml:lang="en">Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-3">
    <aff>
     <institution xml:lang="ru">Национальный исследовательский ядерный университет «МИФИ»</institution>
     <city xml:lang="ru">Москва</city>
     <country country="RU" xml:lang="ru">Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">National Research Nuclear University MEPhI</institution>
     <city xml:lang="en">Moscow</city>
     <country country="RU" xml:lang="en">Russian Federation</country>
    </aff>
   </aff-alternatives>
   <aff-alternatives id="aff-4">
    <aff>
     <institution xml:lang="ru">Национальный исследовательский ядерный университет «МИФИ»</institution>
     <city xml:lang="ru">Москва</city>
     <country country="RU" xml:lang="ru">Россия</country>
    </aff>
    <aff>
     <institution xml:lang="en">National Research Nuclear University MEPhI</institution>
     <city xml:lang="en">Moscow</city>
     <country country="RU" xml:lang="en">Russian Federation</country>
    </aff>
   </aff-alternatives>
   <pub-date publication-format="print" date-type="pub" iso-8601-date="2026-09-19T15:03:28+03:00">
    <day>19</day>
    <month>09</month>
    <year>2026</year>
   </pub-date>
   <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-09-19T15:03:28+03:00">
    <day>19</day>
    <month>09</month>
    <year>2026</year>
   </pub-date>
   <volume>12</volume>
   <issue>3</issue>
   <fpage>54</fpage>
   <lpage>61</lpage>
   <history>
    <date date-type="received" iso-8601-date="2025-12-10T00:00:00+03:00">
     <day>10</day>
     <month>12</month>
     <year>2025</year>
    </date>
    <date date-type="accepted" iso-8601-date="2026-02-26T00:00:00+03:00">
     <day>26</day>
     <month>02</month>
     <year>2026</year>
    </date>
   </history>
   <permissions>
    <copyright-statement xml:lang="ru">© 2026 Лагойда И.А., Воронов С.А., Барбашина Н.С., Астапов И.И.</copyright-statement>
    <copyright-statement xml:lang="en">© 2026 Lagoida I.A., Voronov S.A., Barbashina N.S., Astapov I.I.</copyright-statement>
    <copyright-year>2026</copyright-year>
    <copyright-holder xml:lang="ru">Лагойда Илья Алексеевич, Воронов Сергей Александрович, Барбашина Наталья Сергеевна, Астапов Иван Иванович</copyright-holder>
    <copyright-holder xml:lang="en">Lagoida Ilya Alekseevich, Voronov Sergei Aleksandrovich, Barbashina Natalia Sergeevna, Astapov Ivan Ivanovich</copyright-holder>
   </permissions>
   <self-uri xlink:href="https://zh-szf.ru/en/nauka/publications/6a9c168032807fdbab8763a2/view">https://zh-szf.ru/en/nauka/publications/6a9c168032807fdbab8763a2/view</self-uri>
   <abstract xml:lang="ru">
    <p>Nowadays, there are a large number of ground-based neutron monitors. These detectors measure neutron fluxes produced by the interaction of primary cosmic rays (CR) with Earth’s atmosphere. Since their invention in the 1950s, they have become very popular for studying variations of CR intensity on different time scales. These detection systems are stable and therefore can conduct continuous measurements for decades. However, they exhibit low sensitivity to cosmic ray fluxes with energies ≤1 GeV, whereas heliospheric variations of these fluxes are most pronounced at lower energies. The rapid growth of the space industry has made it possible to perform direct measurements of CR fluxes by a variety of scientific instruments installed on board spacecraft. Satellite-borne detectors measure cosmic ray fluxes across a wide energy range, from tens of keV up to tens of TeV. Nonetheless, experimental data collected by spacecraft is not always immediately accessible and is often published with a significant delay. Moreover, the radiation in outer space is gradually reducing the efficiency and stability of satellite systems, so their operating time in orbit is limited. Ground-based detectors are less susceptible to radiation damage, and their data is always available for scientific research. Therefore, developing methods to reconstruct top-of-atmosphere CR fluxes from ground-based detector data is increasingly urgent. This paper presents the method for calibrating the high-latitude SOPO neutron monitor by machine-learning algorithms, using data on cosmic proton fluxes with energy &gt;500 MeV from the P11 channel of the proton sensor installed aboard the GOES-16 satellite. The machine model obtained as the result of training was employed to reconstruct the low-energy cosmic ray flux from SOPO data. Then it was compared with actual data from the GOES-16 proton sensor.</p>
   </abstract>
   <trans-abstract xml:lang="en">
    <p>Nowadays, there are a large number of ground-based neutron monitors. These detectors measure neutron fluxes produced by the interaction of primary cosmic rays (CR) with Earth’s atmosphere. Since their invention in the 1950s, they have become very popular for studying variations of CR intensity on different time scales. These detection systems are stable and therefore can conduct continuous measurements for decades. However, they exhibit low sensitivity to cosmic ray fluxes with energies ≤1 GeV, whereas heliospheric variations of these fluxes are most pronounced at lower energies. The rapid growth of the space industry has made it possible to perform direct measurements of CR fluxes by a variety of scientific instruments installed on board spacecraft. Satellite-borne detectors measure cosmic ray fluxes across a wide energy range, from tens of keV up to tens of TeV. Nonetheless, experimental data collected by spacecraft is not always immediately accessible and is often published with a significant delay. Moreover, the radiation in outer space is gradually reducing the efficiency and stability of satellite systems, so their operating time in orbit is limited. Ground-based detectors are less susceptible to radiation damage, and their data is always available for scientific research. Therefore, developing methods to reconstruct top-of-atmosphere CR fluxes from ground-based detector data is increasingly urgent. This paper presents the method for calibrating the high-latitude SOPO neutron monitor by machine-learning algorithms, using data on cosmic proton fluxes with energy &gt;500 MeV from the P11 channel of the proton sensor installed aboard the GOES-16 satellite. The machine model obtained as the result of training was employed to reconstruct the low-energy cosmic ray flux from SOPO data. Then it was compared with actual data from the GOES-16 proton sensor.</p>
   </trans-abstract>
   <kwd-group xml:lang="ru">
    <kwd>cosmic rays</kwd>
    <kwd>Forbush decreases</kwd>
    <kwd>geomagnetic storm</kwd>
    <kwd>solar activity</kwd>
   </kwd-group>
   <kwd-group xml:lang="en">
    <kwd>cosmic rays</kwd>
    <kwd>Forbush decreases</kwd>
    <kwd>geomagnetic storm</kwd>
    <kwd>solar activity</kwd>
   </kwd-group>
   <funding-group>
    <funding-statement xml:lang="ru">The work was financially supported by the Ministry of Science and Higher Education of the Russian Federation (Government Assignment No. FSWU-2023-0086)</funding-statement>
    <funding-statement xml:lang="en">The work was financially supported by the Ministry of Science and Higher Education of the Russian Federation (Government Assignment No. FSWU-2023-0086)</funding-statement>
   </funding-group>
  </article-meta>
 </front>
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 </body>
 <back>
  <ref-list>
   <ref id="B1">
    <label>1.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Aguilar M., Cavasonza L.A., Ambrosi G., et al. Periodicities in the daily proton fluxes from 2011 to 2019 measured by the Alpha Magnetic Spectrometer on the International Space Station from 1 to 100 GV. Phys. Rev. Lett. 2021, vol. 127, iss. 27, p. 271102. https://doi.org/10.1103/PhysRevLett.127.271102.</mixed-citation>
     <mixed-citation xml:lang="en">Aguilar M., Cavasonza L.A., Ambrosi G., et al. Periodicities in the daily proton fluxes from 2011 to 2019 measured by the Alpha Magnetic Spectrometer on the International Space Station from 1 to 100 GV. Phys. Rev. Lett. 2021, vol. 127, iss. 27, p. 271102. https://doi.org/10.1103/PhysRevLett.127.271102.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B2">
    <label>2.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Alanko K., Usoskin I.G., Mursula K., et al. Heliospheric modulation strength: effective neutron monitor energy. Adv. Space Res. 2003, vol. 32, iss. 4, pp. 615–620. https://doi.org/10.1016/S0273-1177(03)00348-X.</mixed-citation>
     <mixed-citation xml:lang="en">Alanko K., Usoskin I.G., Mursula K., et al. Heliospheric modulation strength: effective neutron monitor energy. Adv. Space Res. 2003, vol. 32, iss. 4, pp. 615–620. https://doi.org/10.1016/S0273-1177(03)00348-X.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B3">
    <label>3.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Aspinall M.D., Alton T.L., Binnersley C.L., et al. A new ground level neutron monitor for space weather assessment. Scientific Rep. 2024, vol. 14, iss. 1, p. 7174. https://doi.org/10.1038/s41598-024-57583-0.</mixed-citation>
     <mixed-citation xml:lang="en">Aspinall M.D., Alton T.L., Binnersley C.L., et al. A new ground level neutron monitor for space weather assessment. Scientific Rep. 2024, vol. 14, iss. 1, p. 7174. https://doi.org/10.1038/s41598-024-57583-0.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B4">
    <label>4.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Banerjee C., Mukherjee T., Pasiliao Jr.E. An empirical study on generalizations of the ReLU activation function. Proc. ACM southeast conference.  Kennesaw, GA, USA, 2019, pp. 164–167. https://doi.org/10.1145/3299815.3314450.</mixed-citation>
     <mixed-citation xml:lang="en">Banerjee C., Mukherjee T., Pasiliao Jr.E. An empirical study on generalizations of the ReLU activation function. Proc. ACM southeast conference.  Kennesaw, GA, USA, 2019, pp. 164–167. https://doi.org/10.1145/3299815.3314450.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B5">
    <label>5.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Battiston R. High precision cosmic ray physics with AMS-02 on the International Space Station. La Rivista del Nuovo Cimento. 2020, vol. 43, iss. 7, pp. 319–384. https://doi.org/10.1007/s40766-020-00007-2.</mixed-citation>
     <mixed-citation xml:lang="en">Battiston R. High precision cosmic ray physics with AMS-02 on the International Space Station. La Rivista del Nuovo Cimento. 2020, vol. 43, iss. 7, pp. 319–384. https://doi.org/10.1007/s40766-020-00007-2.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B6">
    <label>6.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Blasi P. The origin of galactic cosmic rays. Astron. Astrophys. Rev. 2013, vol. 21, iss. 1, pp. 1–73. https://doi.org/10.1007/s00159-013-0070-7.</mixed-citation>
     <mixed-citation xml:lang="en">Blasi P. The origin of galactic cosmic rays. Astron. Astrophys. Rev. 2013, vol. 21, iss. 1, pp. 1–73. https://doi.org/10.1007/s00159-013-0070-7.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B7">
    <label>7.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Bruno A. Calibration of the GOES 13/15 high‐energy proton detectors based on the PAMELA solar energetic particle observations. Space Weather. 2017, vol. 15, iss. 9, pp. 1191–1202. https://doi.org/10.1002/2017SW001672.</mixed-citation>
     <mixed-citation xml:lang="en">Bruno A. Calibration of the GOES 13/15 high‐energy proton detectors based on the PAMELA solar energetic particle observations. Space Weather. 2017, vol. 15, iss. 9, pp. 1191–1202. https://doi.org/10.1002/2017SW001672.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B8">
    <label>8.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Bruno A., Bazilevskaya G.A., Boezio M., et al. Solar energetic particle events observed by the PAMELA mission. Astrophys. J. 2018, vol. 862, iss. 2, p. 97. https://doi.org/10.3847/1538-4357/aacc26.</mixed-citation>
     <mixed-citation xml:lang="en">Bruno A., Bazilevskaya G.A., Boezio M., et al. Solar energetic particle events observed by the PAMELA mission. Astrophys. J. 2018, vol. 862, iss. 2, p. 97. https://doi.org/10.3847/1538-4357/aacc26.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B9">
    <label>9.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Bykov A.M., Ellison D.C., Marcowith A., et al. Cosmic ray production in supernovae. Space Sci. Rev. 2018, vol. 214, iss. 1, p. 41. https://doi.org/10.1007/s11214-018-0479-4.</mixed-citation>
     <mixed-citation xml:lang="en">Bykov A.M., Ellison D.C., Marcowith A., et al. Cosmic ray production in supernovae. Space Sci. Rev. 2018, vol. 214, iss. 1, p. 41. https://doi.org/10.1007/s11214-018-0479-4.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B10">
    <label>10.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Caballero‐Lopez R.A., Moraal H. Limitations of the force field equation to describe cosmic ray modulation. J. Geophys. Res.: Space Phys. 2004, vol. 109, iss. A1, p. A01101. https://doi.org/10.1029/2003JA010098.</mixed-citation>
     <mixed-citation xml:lang="en">Caballero‐Lopez R.A., Moraal H. Limitations of the force field equation to describe cosmic ray modulation. J. Geophys. Res.: Space Phys. 2004, vol. 109, iss. A1, p. A01101. https://doi.org/10.1029/2003JA010098.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B11">
    <label>11.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Calligaro C., Gatti U. Rad-hard Semiconductor Memories. River Publishers, 2018, 416 p. https://doi.org/10.1201/9781003339182-1.</mixed-citation>
     <mixed-citation xml:lang="en">Calligaro C., Gatti U. Rad-hard Semiconductor Memories. River Publishers, 2018, 416 p. https://doi.org/10.1201/9781003339182-1.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B12">
    <label>12.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Cane H.V. Coronal mass ejections and Forbush decreases. Space Sci. Rev. 2000, vol. 93, iss. 1, pp. 55–77. https://doi.org/10.1023/A:1026532125747.</mixed-citation>
     <mixed-citation xml:lang="en">Cane H.V. Coronal mass ejections and Forbush decreases. Space Sci. Rev. 2000, vol. 93, iss. 1, pp. 55–77. https://doi.org/10.1023/A:1026532125747.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B13">
    <label>13.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Chu W., Yang Y., Xu S., et al. Study on long-term variation characteristics of geomagnetic cutoff rigidities of energetic protons caused by long-term variation of geomagnetic field. Frontiers in Earth Science. 2022, vol. 10, p. 818788. https://doi.org/10.3389/feart.2022.818788.</mixed-citation>
     <mixed-citation xml:lang="en">Chu W., Yang Y., Xu S., et al. Study on long-term variation characteristics of geomagnetic cutoff rigidities of energetic protons caused by long-term variation of geomagnetic field. Frontiers in Earth Science. 2022, vol. 10, p. 818788. https://doi.org/10.3389/feart.2022.818788.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B14">
    <label>14.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Curto J.J. Geomagnetic solar flare effects: A review. J. Space Weather and Space Climate. 2020, vol. 10, p. 27. https://doi.org/10.1051/swsc/2020027.</mixed-citation>
     <mixed-citation xml:lang="en">Curto J.J. Geomagnetic solar flare effects: A review. J. Space Weather and Space Climate. 2020, vol. 10, p. 27. https://doi.org/10.1051/swsc/2020027.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B15">
    <label>15.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Desai M., Giacalone J. Large gradual solar energetic particle events. Living Rev. in Solar Phys. 2016, vol. 13, iss. 1, p. 3. https://doi.org/10.1007/s41116-016-0002-5.</mixed-citation>
     <mixed-citation xml:lang="en">Desai M., Giacalone J. Large gradual solar energetic particle events. Living Rev. in Solar Phys. 2016, vol. 13, iss. 1, p. 3. https://doi.org/10.1007/s41116-016-0002-5.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B16">
    <label>16.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Dong X.L., Yao Y.H., Guo Y.Q., et al. New understanding of nuclei spectra properties observed by the AMS-02 experiment. Phys. Rev. D. 2024, vol. 109, iss. 6, p. 063027. https://doi.org/10.1103/PhysRevD.109.063027.</mixed-citation>
     <mixed-citation xml:lang="en">Dong X.L., Yao Y.H., Guo Y.Q., et al. New understanding of nuclei spectra properties observed by the AMS-02 experiment. Phys. Rev. D. 2024, vol. 109, iss. 6, p. 063027. https://doi.org/10.1103/PhysRevD.109.063027.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B17">
    <label>17.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Gabici S. Low-energy cosmic rays: Regulators of the dense interstellar medium. Astron. Astrophys. Rev. 2022, vol. 30, iss. 1, p. 4. https://doi.org/10.1007/s00159-022-00141-2.</mixed-citation>
     <mixed-citation xml:lang="en">Gabici S. Low-energy cosmic rays: Regulators of the dense interstellar medium. Astron. Astrophys. Rev. 2022, vol. 30, iss. 1, p. 4. https://doi.org/10.1007/s00159-022-00141-2.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B18">
    <label>18.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Gleeson L.J., Axford W.I. Solar modulation of galactic cosmic rays. Astrophys. J. 1968, vol. 154, p. 1011. https://doi.org/10.1086/149822.</mixed-citation>
     <mixed-citation xml:lang="en">Gleeson L.J., Axford W.I. Solar modulation of galactic cosmic rays. Astrophys. J. 1968, vol. 154, p. 1011. https://doi.org/10.1086/149822.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B19">
    <label>19.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Goodman S.J., Schmit T.J., Daniels J., et al. The GOES-R series: A new generation of geostationary environmental satellites. Elsevier, 2020, pp. 243–250. https://10.1016/B978-0-12-814327-8.00019-3.</mixed-citation>
     <mixed-citation xml:lang="en">Goodman S.J., Schmit T.J., Daniels J., et al. The GOES-R series: A new generation of geostationary environmental satellites. Elsevier, 2020, pp. 243–250. https://10.1016/B978-0-12-814327-8.00019-3.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B20">
    <label>20.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Gopalswamy N., Yashiro S., Michalek G., et al. The SOHO/LASCO CME catalog. Earth, Moon, and Planets. 2009, vol. 104, iss. 1, pp. 295–313.  https://doi.org/10.1007/s11038-008-9282-7.</mixed-citation>
     <mixed-citation xml:lang="en">Gopalswamy N., Yashiro S., Michalek G., et al. The SOHO/LASCO CME catalog. Earth, Moon, and Planets. 2009, vol. 104, iss. 1, pp. 295–313.  https://doi.org/10.1007/s11038-008-9282-7.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B21">
    <label>21.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Hatton C.J., Carmichael H. Experimental investigation of the NM-64 neutron monitor. Canadian J. Phys. 1964, vol. 42, iss. 12, pp. 2443–2472. https://doi.org/10.1139/p64-222.</mixed-citation>
     <mixed-citation xml:lang="en">Hatton C.J., Carmichael H. Experimental investigation of the NM-64 neutron monitor. Canadian J. Phys. 1964, vol. 42, iss. 12, pp. 2443–2472. https://doi.org/10.1139/p64-222.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B22">
    <label>22.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Hu S., Semones E. Calibration of the GOES 6–16 high-energy proton detectors based on modelling of ground level enhancement energy spectra. J. Space Weather and Space Climate. 2022, vol. 12, p. 5. https://doi.org/10.1051/swsc/2022003.</mixed-citation>
     <mixed-citation xml:lang="en">Hu S., Semones E. Calibration of the GOES 6–16 high-energy proton detectors based on modelling of ground level enhancement energy spectra. J. Space Weather and Space Climate. 2022, vol. 12, p. 5. https://doi.org/10.1051/swsc/2022003.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B23">
    <label>23.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Kilpua E., Koskinen H.E., Pulkkinen T.I. Coronal mass ejections and their sheath regions in interplanetary space. Living Rev. Solar Phys. 2017, vol. 14, iss. 1, p. 5. https://doi.org/10.1007/s41116-017-0009-6.</mixed-citation>
     <mixed-citation xml:lang="en">Kilpua E., Koskinen H.E., Pulkkinen T.I. Coronal mass ejections and their sheath regions in interplanetary space. Living Rev. Solar Phys. 2017, vol. 14, iss. 1, p. 5. https://doi.org/10.1007/s41116-017-0009-6.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B24">
    <label>24.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Kingma D.P., Ba J. Adam: A method for stochastic optimization. Proc. International Conference on Learning Representations (ICLR). San Diego, CA, USA, 2014. https://doi.org/10.48550/arXiv.1412.6980.</mixed-citation>
     <mixed-citation xml:lang="en">Kingma D.P., Ba J. Adam: A method for stochastic optimization. Proc. International Conference on Learning Representations (ICLR). San Diego, CA, USA, 2014. https://doi.org/10.48550/arXiv.1412.6980.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B25">
    <label>25.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Koldobskiy S.A, Usoskin I.G. Reconstruction of solar modulation potential from AMS-02 daily data for the period 2011–2019 and its intercomparison with indirect cosmic-ray measurements. Proc. 38th International Cosmic Ray Conference. Nagoya, Japan, 2024, p. 1325. https://doi.org/10.22323/1.444.1325.</mixed-citation>
     <mixed-citation xml:lang="en">Koldobskiy S.A, Usoskin I.G. Reconstruction of solar modulation potential from AMS-02 daily data for the period 2011–2019 and its intercomparison with indirect cosmic-ray measurements. Proc. 38th International Cosmic Ray Conference. Nagoya, Japan, 2024, p. 1325. https://doi.org/10.22323/1.444.1325.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B26">
    <label>26.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Kress B.T., Rodriguez J.V., Boudouridis A., et al. Observations from NOAA’s newest solar proton sensor. Space Weather. 2021, vol. 19, iss. 12, p. e2021SW002750. https://doi.org/10.1029/2021SW002750.</mixed-citation>
     <mixed-citation xml:lang="en">Kress B.T., Rodriguez J.V., Boudouridis A., et al. Observations from NOAA’s newest solar proton sensor. Space Weather. 2021, vol. 19, iss. 12, p. e2021SW002750. https://doi.org/10.1029/2021SW002750.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B27">
    <label>27.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Lagoida I.A., Voronov S.A., Mikhailov V.V. Features of Forbush decreases according to satellite and ground based detectors. Physics of Atomic Nuclei. 2024, vol. 87, iss. 2, pp. 86–92. https://doi.org/10.1134/S1063778824020133.</mixed-citation>
     <mixed-citation xml:lang="en">Lagoida I.A., Voronov S.A., Mikhailov V.V. Features of Forbush decreases according to satellite and ground based detectors. Physics of Atomic Nuclei. 2024, vol. 87, iss. 2, pp. 86–92. https://doi.org/10.1134/S1063778824020133.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B28">
    <label>28.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Lau M.M., Hann L.K. Review of adaptive activation function in deep neural networks. Proc. Conference on Biomedical Engineering and Sciences (IECBES). Sarawak, Malaysia, 2018, pp. 686–690. https://doi.org/10.1109/IECBES.2018.8626714.</mixed-citation>
     <mixed-citation xml:lang="en">Lau M.M., Hann L.K. Review of adaptive activation function in deep neural networks. Proc. Conference on Biomedical Engineering and Sciences (IECBES). Sarawak, Malaysia, 2018, pp. 686–690. https://doi.org/10.1109/IECBES.2018.8626714.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B29">
    <label>29.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Lederer J. Activation functions in artificial neural networks: A systematic overview. arXiv preprint arXiv:2101.09957. 2021. https://arxiv.org/abs/2101.09957.</mixed-citation>
     <mixed-citation xml:lang="en">Lederer J. Activation functions in artificial neural networks: A systematic overview. arXiv preprint arXiv:2101.09957. 2021. https://arxiv.org/abs/2101.09957.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B30">
    <label>30.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Mertens C.J., Tobiska W.K. Space weather radiation effects on high-altitude/latitude aircraft. Space Weather Effects and Applications. Wiley, 2021, pp. 79–110. https://doi.org/10.1002/9781119815570.ch4.</mixed-citation>
     <mixed-citation xml:lang="en">Mertens C.J., Tobiska W.K. Space weather radiation effects on high-altitude/latitude aircraft. Space Weather Effects and Applications. Wiley, 2021, pp. 79–110. https://doi.org/10.1002/9781119815570.ch4.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B31">
    <label>31.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Miroshnichenko L.I. Solar cosmic rays: 75 years of research. Physics-Uspekhi. 2018, vol. 61, iss. 4, p. 323. https://doi.org/10.3367/UFNe.2017.03.038091.</mixed-citation>
     <mixed-citation xml:lang="en">Miroshnichenko L.I. Solar cosmic rays: 75 years of research. Physics-Uspekhi. 2018, vol. 61, iss. 4, p. 323. https://doi.org/10.3367/UFNe.2017.03.038091.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B32">
    <label>32.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Mishev A.L., Koldobskiy S.A., Kovaltsov G.A., et al. Updated neutron‐monitor yield function: Bridging between in situ and ground‐based cosmic ray measurements. J. Geophys. Res.: Space Phys. 2020, vol. 125, iss. 2, p. e2019JA027433. https://doi.org/10.1029/2019JA027433.</mixed-citation>
     <mixed-citation xml:lang="en">Mishev A.L., Koldobskiy S.A., Kovaltsov G.A., et al. Updated neutron‐monitor yield function: Bridging between in situ and ground‐based cosmic ray measurements. J. Geophys. Res.: Space Phys. 2020, vol. 125, iss. 2, p. e2019JA027433. https://doi.org/10.1029/2019JA027433.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B33">
    <label>33.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Mishev A.L., Poluianov S. About the altitude profile of the atmospheric cut-off of cosmic rays: new revised assessment. Solar Phys. 2021, vol. 296, iss. 8, p. 129. https://doi.org/10.1007/s11207-021-01875-5.</mixed-citation>
     <mixed-citation xml:lang="en">Mishev A.L., Poluianov S. About the altitude profile of the atmospheric cut-off of cosmic rays: new revised assessment. Solar Phys. 2021, vol. 296, iss. 8, p. 129. https://doi.org/10.1007/s11207-021-01875-5.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B34">
    <label>34.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Moraal H. Cosmic-ray modulation equations. Space Sci. Rev. 2013, vol. 176, iss. 1, pp. 299–319. https://doi.org/10.1007/s11214-011-9819-3.</mixed-citation>
     <mixed-citation xml:lang="en">Moraal H. Cosmic-ray modulation equations. Space Sci. Rev. 2013, vol. 176, iss. 1, pp. 299–319. https://doi.org/10.1007/s11214-011-9819-3.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B35">
    <label>35.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Netrapalli P. Stochastic gradient descent and its variants in machine learning. J. Indian Institute of Science. 2019, vol. 99, iss. 2, pp. 201–213. https://doi.org/10.1007/s41745-019-0098-4.</mixed-citation>
     <mixed-citation xml:lang="en">Netrapalli P. Stochastic gradient descent and its variants in machine learning. J. Indian Institute of Science. 2019, vol. 99, iss. 2, pp. 201–213. https://doi.org/10.1007/s41745-019-0098-4.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B36">
    <label>36.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Nielsen M.A. Neural Networks and Deep Learning. San Francisco, CA, USA, Determination press, 2015, 281 p.</mixed-citation>
     <mixed-citation xml:lang="en">Nielsen M.A. Neural Networks and Deep Learning. San Francisco, CA, USA, Determination press, 2015, 281 p.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B37">
    <label>37.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Oh S.Y., Bieber J.W., Clem J., et al. South Pole neutron monitor forecasting of solar proton radiation intensity. Space Weather. 2012, vol. 10, iss. 5, p. S05004. https://doi.org/10.1029/2012SW000795.</mixed-citation>
     <mixed-citation xml:lang="en">Oh S.Y., Bieber J.W., Clem J., et al. South Pole neutron monitor forecasting of solar proton radiation intensity. Space Weather. 2012, vol. 10, iss. 5, p. S05004. https://doi.org/10.1029/2012SW000795.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B38">
    <label>38.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Picozza P., Spillantini P., Marcelli L. Cosmic ray direct measurements. Nuclear and Particle Physics Proc. 2018, vol. 297, pp. 207–215. https://doi.org/10.1016/j.nuclphysbps.2018.07.030.</mixed-citation>
     <mixed-citation xml:lang="en">Picozza P., Spillantini P., Marcelli L. Cosmic ray direct measurements. Nuclear and Particle Physics Proc. 2018, vol. 297, pp. 207–215. https://doi.org/10.1016/j.nuclphysbps.2018.07.030.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B39">
    <label>39.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Poluianov S., Batalla O. Cosmic-ray atmospheric cutoff energies of polar neutron monitors. Adv. Space Res. 20–22, vol. 70, iss. 9, pp. 2610–2617. https://doi.org/10.1016/j.asr.2022.03.037.</mixed-citation>
     <mixed-citation xml:lang="en">Poluianov S., Batalla O. Cosmic-ray atmospheric cutoff energies of polar neutron monitors. Adv. Space Res. 20–22, vol. 70, iss. 9, pp. 2610–2617. https://doi.org/10.1016/j.asr.2022.03.037.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B40">
    <label>40.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Potgieter M.S. Solar modulation of cosmic rays. Living Rev. in Solar Phys. 2013, vol. 10, iss. 1, p. 3. https://doi.org/10.12942/lrsp-2013-3.</mixed-citation>
     <mixed-citation xml:lang="en">Potgieter M.S. Solar modulation of cosmic rays. Living Rev. in Solar Phys. 2013, vol. 10, iss. 1, p. 3. https://doi.org/10.12942/lrsp-2013-3.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B41">
    <label>41.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Potgieter M.S. The charge-sign dependent effect in the solar modulation of cosmic rays. Adv. Space Res. 2014, vol. 53, iss. 10, pp. 1415–1425. https://doi.org/10.1016/j.asr.2013.04.015.</mixed-citation>
     <mixed-citation xml:lang="en">Potgieter M.S. The charge-sign dependent effect in the solar modulation of cosmic rays. Adv. Space Res. 2014, vol. 53, iss. 10, pp. 1415–1425. https://doi.org/10.1016/j.asr.2013.04.015.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B42">
    <label>42.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Ptuskin V. Propagation of galactic cosmic rays. Astroparticle Physics. 2012, vol. 39, pp. 44–51. https://doi.org/10.1016/j.astropartphys.2011.11.004.</mixed-citation>
     <mixed-citation xml:lang="en">Ptuskin V. Propagation of galactic cosmic rays. Astroparticle Physics. 2012, vol. 39, pp. 44–51. https://doi.org/10.1016/j.astropartphys.2011.11.004.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B43">
    <label>43.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Riggi F. The Detection of Extensive Air Showers. Springer, 2023, pp. 155–171. https://doi.org/10.1007/978-3-031-24762-0.</mixed-citation>
     <mixed-citation xml:lang="en">Riggi F. The Detection of Extensive Air Showers. Springer, 2023, pp. 155–171. https://doi.org/10.1007/978-3-031-24762-0.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B44">
    <label>44.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Rozelot J.P., Elchin S, Babayev E.S. Variability of the Sun and Sun-like Stars: From Asteroseismology to Space Weather. EDP Sciences, 2018, 238 p. https://doi.org/10.1051/978-2-7598-2196-9.</mixed-citation>
     <mixed-citation xml:lang="en">Rozelot J.P., Elchin S, Babayev E.S. Variability of the Sun and Sun-like Stars: From Asteroseismology to Space Weather. EDP Sciences, 2018, 238 p. https://doi.org/10.1051/978-2-7598-2196-9.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B45">
    <label>45.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Siruk S.A., Alexandrin S.U., Lagoida I.A., et al. Mountainous regions of the Russian Arctic as a platform for space weather research Sol.-Terr. Phys. 2025, vol. 11, iss. 2, pp. 139–143. DOI: 10.12737/stp-112202513.</mixed-citation>
     <mixed-citation xml:lang="en">Siruk S.A., Alexandrin S.U., Lagoida I.A., et al. Mountainous regions of the Russian Arctic as a platform for space weather research Sol.-Terr. Phys. 2025, vol. 11, iss. 2, pp. 139–143. DOI: 10.12737/stp-112202513.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B46">
    <label>46.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Strauss D.T., Poluianov S., Van Der Merwe C., et al. The mini-neutron monitor: A new approach in neutron monitor design. J. Space Weather and Space Climate. 2020, vol. 10, p. 39. https://doi.org/10.1051/swsc/2020038.</mixed-citation>
     <mixed-citation xml:lang="en">Strauss D.T., Poluianov S., Van Der Merwe C., et al. The mini-neutron monitor: A new approach in neutron monitor design. J. Space Weather and Space Climate. 2020, vol. 10, p. 39. https://doi.org/10.1051/swsc/2020038.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B47">
    <label>47.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Tomsia M., Cieśla J., Śmieszek J., et al. Long-term space missions effects on the human organism: what we do know and what requires further research. Annals of Agricultural and Environmental Medicine. 2024, vol. 31, iss. 2, pp. 175–181. https://doi.org/10.26444/aaem/186595.</mixed-citation>
     <mixed-citation xml:lang="en">Tomsia M., Cieśla J., Śmieszek J., et al. Long-term space missions effects on the human organism: what we do know and what requires further research. Annals of Agricultural and Environmental Medicine. 2024, vol. 31, iss. 2, pp. 175–181. https://doi.org/10.26444/aaem/186595.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B48">
    <label>48.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Usoskin I.G., Alanko‐Huotari K., Kovaltsov G.A., et al. Helio-spheric modulation of cosmic rays: Monthly reconstruction for 1951–2004. J. Geophys. Res.: Space Phys. 2005, vol. 110, iss. A12, p. A12108. https://doi.org/10.1029/2005JA011250.</mixed-citation>
     <mixed-citation xml:lang="en">Usoskin I.G., Alanko‐Huotari K., Kovaltsov G.A., et al. Helio-spheric modulation of cosmic rays: Monthly reconstruction for 1951–2004. J. Geophys. Res.: Space Phys. 2005, vol. 110, iss. A12, p. A12108. https://doi.org/10.1029/2005JA011250.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B49">
    <label>49.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Väisänen P., Usoskin I., Kähkönen R., et al. Revised reconstruction of the heliospheric modulation potential for 1964–2022. J. Geophys. Res.: Space Phys. 2023, vol. 128, iss. 4, p. e2023JA031352. https://doi.org/10.1029/2023JA031352.</mixed-citation>
     <mixed-citation xml:lang="en">Väisänen P., Usoskin I., Kähkönen R., et al. Revised reconstruction of the heliospheric modulation potential for 1964–2022. J. Geophys. Res.: Space Phys. 2023, vol. 128, iss. 4, p. e2023JA031352. https://doi.org/10.1029/2023JA031352.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B50">
    <label>50.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Wang Q., Ma Y., Zhao K. A comprehensive survey of loss functions in machine learning. Annals of Data Science. 2022, vol. 9, iss. 2, pp. 187–212. https://doi.org/10.1007/s40745-020-00253-5.</mixed-citation>
     <mixed-citation xml:lang="en">Wang Q., Ma Y., Zhao K. A comprehensive survey of loss functions in machine learning. Annals of Data Science. 2022, vol. 9, iss. 2, pp. 187–212. https://doi.org/10.1007/s40745-020-00253-5.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B51">
    <label>51.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">Zhang N., Shen S.L., Zhou A., et al. Investigation on performance of neural networks using quadratic relative error cost function. IEEE Access. 2019, vol. 7, pp. 106642–106652. https://doi.org/10.1109/ACCESS.2019.2930520.</mixed-citation>
     <mixed-citation xml:lang="en">Zhang N., Shen S.L., Zhou A., et al. Investigation on performance of neural networks using quadratic relative error cost function. IEEE Access. 2019, vol. 7, pp. 106642–106652. https://doi.org/10.1109/ACCESS.2019.2930520.</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B52">
    <label>52.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">URL: https://www.airbus.com/en/newsroom/press-releases/2025-11-airbus-update-on-a320-family-precautionary-fleet-action (accessed May 12, 2026).</mixed-citation>
     <mixed-citation xml:lang="en">URL: https://www.airbus.com/en/newsroom/press-releases/2025-11-airbus-update-on-a320-family-precautionary-fleet-action (accessed May 12, 2026).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B53">
    <label>53.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">URL: https://omniweb.gsfc.nasa.gov/form/dx1.html (accessed May 12, 2026).</mixed-citation>
     <mixed-citation xml:lang="en">URL: https://omniweb.gsfc.nasa.gov/form/dx1.html (accessed May 12, 2026).</mixed-citation>
    </citation-alternatives>
   </ref>
   <ref id="B54">
    <label>54.</label>
    <citation-alternatives>
     <mixed-citation xml:lang="ru">URL: https://github.com/fchollet/keras (accessed May 12, 2026).</mixed-citation>
     <mixed-citation xml:lang="en">URL: https://github.com/fchollet/keras (accessed May 12, 2026).</mixed-citation>
    </citation-alternatives>
   </ref>
  </ref-list>
 </back>
</article>
