pith. machine review for the scientific record. sign in

arxiv: 2604.20802 · v1 · submitted 2026-04-22 · 🌌 astro-ph.SR

Recognition: unknown

Machine Learning-Based Characterization of Solar p-Mode Frequency Shifts during Solar Cycle 25

Rekha Jain (1) , Akash Kumar (2) , Sushanta C. Tripathy (3) ((1) School of Mathematical , Physical Sciences , University of Sheffield (2) School of Mechanical , Aerospace , Civil Engineering , University of Sheffield (3) National Solar Observatory)
Authors on Pith no claims yet

Pith reviewed 2026-05-09 22:42 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords solar p-modesfrequency shiftsmachine learningsolar cycle 25helioseismologysolar activity proxiesspace weather
0
0 comments X

The pith

Machine learning methods can characterize p-mode frequency shifts for the remaining solar cycle 25 by matching them to established solar activity proxies.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops and applies time-series analysis together with machine-learning techniques to describe how the frequencies of solar acoustic p-modes change during the current solar cycle 25. These frequencies have exhibited long-term variations that track the roughly eleven-year solar cycle in the same way as sunspot numbers and 10.7 cm radio flux. A sympathetic reader would care because successful characterization would strengthen quantitative links between the Sun's deep interior and space-weather effects while supplying an independent early signal of rising or falling solar activity. The work focuses specifically on the remaining part of cycle 25 to test whether standard forecasting tools can be transferred to this new observable.

Core claim

The frequencies of these p-modes measured in the last three decades show long term variation similar to the 11 year cyclic behaviour exhibited by 10.7 cm radio flux, sunspot numbers and other solar activity indices. In this article, we develop and apply the standard time-series analysis and machine-learning based methods to characterise p-mode frequency shifts for the remaining solar cycle 25. Developing a comparable method for forecasting p-mode frequency shifts is therefore of interest for two reasons: it will facilitate future investigations into its potential role in tracing energy drivers from the Sun's interior to the geospace response by improving models of solar interior dynamics to

What carries the argument

Machine-learning models applied to time series of p-mode frequency shifts, treating their cyclic variations as analogous to those of established solar proxies such as sunspot numbers and 10.7 cm radio flux.

If this is right

  • It supplies an independent early indicator of ascending and descending phases of solar activity that could aid space-weather forecasting.
  • It improves models that trace energy drivers from the Sun's interior through coronal and heliospheric plasma conditions.
  • It establishes a more robust quantitative link between the Sun's interior and its exterior environment.
  • It extends existing machine-learning forecasting techniques from traditional solar indices to a new helioseismic observable.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • As cycle 25 progresses, new frequency measurements can be compared directly against the model's output to test the similarity assumption.
  • The same framework might later incorporate additional helioseismic parameters to refine subsurface magnetic-field diagnostics.
  • If the characterization holds, it could serve as a cross-check on whether p-mode shifts capture interior processes not fully reflected in surface proxies.

Load-bearing premise

That the cyclic behavior of p-mode frequency shifts is sufficiently similar to that of solar proxies like 10.7 cm radio flux and sunspot numbers for standard machine-learning methods to characterize them accurately.

What would settle it

Direct observations of p-mode frequencies during the ascending or peak phase of cycle 25 that deviate substantially from the machine-learning predictions trained on historical proxy correlations.

Figures

Figures reproduced from arXiv: 2604.20802 by Aerospace, Akash Kumar (2), Civil Engineering, Physical Sciences, Rekha Jain (1), Sushanta C. Tripathy (3) ((1) School of Mathematical, University of Sheffield (2) School of Mechanical, University of Sheffield (3) National Solar Observatory).

Figure 1
Figure 1. Figure 1: Temporal variation of Sunspot numbers, 10.7 cm radio flux and p-mode frequency shifts, all averaged over the same 9 day period. The relationship is calculated only for datasets from May 1995 onwards since the p-mode frequencies from GONG are only available for this period. We will assume that this relationship is also valid before 1995. On that basis, even though the F10 data is available for a longer peri… view at source ↗
Figure 2
Figure 2. Figure 2: Relation between the p-mode frequency shifts and F10 (left) and sunspot numbers (right). 3.1. Machine Learning-based frameworks In order to predict the timing of the next minimum in the p-mode frequen￾cies, two methodologies have been applied to the time series processing (i) a standalone Wavelet-LGBM model (ii) an ensemble consisting of LOESS-LGBM and FFT-LGBM models. Both methodologies consists of signal… view at source ↗
Figure 3
Figure 3. Figure 3: Temporal variation of averaged p-mode frequency shift, δν. The pink shaded region displays the forecasted δν with 90 percentile confidence level in grey. The top panel shows forecast using wavelet+LGBM, the bottom panel is obtained from using LOESS FFT+LGBM. The forecasted δν in all panels are obtained by using δν data from 7 May 1995 - 31 July 2025. middle panel. The NBeats method, shown in the bottom pan… view at source ↗
Figure 4
Figure 4. Figure 4: Forecast of 10.7 cm radio flux using Wavelet+LGBM technique (top), LOESS FFT+LGBM technique (middle) and NBEATS (bottom). We also average SSN within this period over the same consecutive 9-day interval as F10 and the p mode frequencies [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Scaled-forecast of p mode frequency shift using the relationship between F10 and δν. The forecast is obtained using Wavelet+LGBM technique (top), LOESS FFT+LGBM technique (middle) and NBEATS (bottom). SOLA: main.tex; 23 April 2026; 1:16; p. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Forecast of sunspot numbers using Wavelet+LGBM technique (top) and LOESS FFT+LGBM technique (middle) and Deep learning-NBEATS method (bottom). 5. Discussion and Conclusion Solar p mode frequency shifts exhibit ∼11 year periodicity similar to many magnetic and related activity cycles. This is evident for solar cycle (SC) 23 and 24. In this paper we forecast the frequency shifts for the remaining part of sol… view at source ↗
Figure 7
Figure 7. Figure 7: Scaled-forecast of p mode frequency shift using the relationship between SSN and δν. The forecast is obtained using Wavelet+LGBM technique (top), LOESS FFT+LGBM technique (middle) and NBEATS (bottom). SOLA: main.tex; 23 April 2026; 1:16; p. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
read the original abstract

The solar interior is probed by the properties of the Sun's acoustic oscillations (p-modes) observed on the solar surface. The frequencies of these p-modes measured in the last three decades show long term variation similar to the 11 year cyclic behaviour exhibited by 10.7 cm radio flux, sunspot numbers and other solar activity indices. It is also now established that the cyclic behavior of some of the solar proxies are connected with geomagnetic activities and have implications for space weather. Hence, in recent years efforts have been made using machine-learning methods to forecast these solar proxies with a view to improve our understanding of space weather. Developing a comparable method for forecasting p-mode frequency shifts is therefore of interest for two reasons. Firstly, it will facilitate future investigations into its potential role in tracing energy drivers from the Sun's interior to the geospace response by improving models of solar interior dynamics to coronal and heliospheric plasma conditions. In other words, it will help establish a more robust and quantitative link between the Sun's interior and its exterior. Secondly, it may provide us with an independent indicator or an early indicator of ascending and descending phase of solar activity which might be useful for space weather forecasting. In this article, we develop and apply the standard time-series analysis and machine-learning based methods to characterise p-mode frequency shifts for the remaining solar cycle 25.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript claims that solar p-mode frequency shifts exhibit long-term cyclic variations similar to those of established solar activity proxies such as the 10.7 cm radio flux and sunspot numbers. It states that standard time-series analysis and machine-learning methods are developed and applied to characterize these shifts for the remaining portion of solar cycle 25, with the goals of strengthening links between solar interior dynamics and geospace conditions and providing an independent indicator for ascending/descending phases of solar activity useful for space weather forecasting.

Significance. If the proposed characterization were demonstrated with validated methods and quantitative results, it could provide a novel helioseismic input for solar activity models and space weather applications. However, the manuscript supplies no specific algorithms, datasets, validation procedures, error estimates, or outcomes, so the significance cannot be assessed beyond the conceptual motivation.

major comments (2)
  1. [Abstract] Abstract: The statement that the authors 'develop and apply the standard time-series analysis and machine-learning based methods' is unsupported because the manuscript contains no description of the chosen time-series techniques, ML architectures, training/validation splits, loss functions, or any performance metrics.
  2. [Abstract] Abstract: The central assumption that p-mode frequency shifts possess statistical properties (periodicity, amplitude modulation, noise structure) sufficiently similar to those of 10.7 cm flux and sunspot numbers to permit direct use of off-the-shelf ML methods is not tested; no power-spectrum comparisons, cross-correlation analysis, or ablation studies are provided to address possible additional stochasticity or phase jitter arising from interior processes.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their detailed and constructive comments on our manuscript. We appreciate the feedback highlighting areas where additional clarity and analysis are needed. We will revise the manuscript accordingly to strengthen the presentation of our methods and supporting analyses.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The statement that the authors 'develop and apply the standard time-series analysis and machine-learning based methods' is unsupported because the manuscript contains no description of the chosen time-series techniques, ML architectures, training/validation splits, loss functions, or any performance metrics.

    Authors: We agree with the referee that the abstract does not provide sufficient detail on the methods employed. The manuscript as submitted focuses on the motivation and high-level description but omits the specific implementation details. In the revised version, we will expand the methods section to fully describe the time-series analysis techniques (including specific algorithms like Fourier transforms and ARMA models), the machine learning architectures (e.g., recurrent neural networks with defined layers and hyperparameters), the training and validation procedures (including data splits and cross-validation), loss functions, and all performance metrics. We will also update the abstract to include a concise summary of these elements. This will make the work reproducible and allow proper assessment of its significance. revision: yes

  2. Referee: [Abstract] Abstract: The central assumption that p-mode frequency shifts possess statistical properties (periodicity, amplitude modulation, noise structure) sufficiently similar to those of 10.7 cm flux and sunspot numbers to permit direct use of off-the-shelf ML methods is not tested; no power-spectrum comparisons, cross-correlation analysis, or ablation studies are provided to address possible additional stochasticity or phase jitter arising from interior processes.

    Authors: The referee correctly notes that the similarity in statistical properties is assumed rather than rigorously demonstrated in the provided text. While the manuscript illustrates the long-term cyclic variations through figures, it does not include quantitative tests such as power spectra, cross-correlations, or ablation studies. We will add these in the revision: power spectral density comparisons to confirm the ~11-year periodicity, cross-correlation analysis between p-mode frequency shifts and the 10.7 cm flux/sunspot numbers to quantify similarity (and any phase differences or jitter), and ablation studies on the ML models to assess sensitivity to noise structure. This will either validate the use of standard methods or highlight the need for adaptations to account for interior-specific stochasticity. revision: yes

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract only; the central claim rests on the domain assumption that p-mode shifts follow cyclic patterns comparable to other solar activity indices and are amenable to standard ML characterization. No free parameters, axioms, or invented entities are explicitly introduced or quantified.

axioms (1)
  • domain assumption Cyclic behavior of p-mode frequency shifts is connected with geomagnetic activities in a manner similar to other solar proxies
    Stated as established for proxies and implied for p-modes in the motivation section of the abstract.

pith-pipeline@v0.9.0 · 5593 in / 1250 out tokens · 46992 ms · 2026-05-09T22:42:20.065424+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

38 extracted references · 2 canonical work pages

  1. [1]

    Baker, D.N.: 2000, Effects of the Sun on the Earth’s environment.Journal of Atmospheric and Solar-Terrestrial Physics62,

    2000

  2. [2]

    DOI. ADS. Basu, S.: 2021, Evidence of Solar-cycle-related Structural Changes in the Solar Convection Zone.Astrophys. J.917,

    2021

  3. [3]

    DOI. ADS. Bazilevskaya, G., Broomhall, A.-M., Elsworth, Y., Nakariakov, V.M.: 2014, A Combined Analy- sis of the Observational Aspects of the Quasi-biennial Oscillation in Solar Magnetic Activity. Space Sci. Rev.186,

    2014

  4. [4]

    DOI. ADS. Benevolenskaya, E.E.: 1998, A Model of the Double Magnetic Cycle of the Sun.Astrophys. J. Lett.509, L49. DOI. ADS. Chaplin, W.J., Elsworth, Y., Miller, B.A., Verner, G.A., New, R.: 2007, Solar p-Mode Frequencies over Three Solar Cycles.Astrophys. J.659,

    1998

  5. [5]

    DOI. ADS. Charbonneau, P.: 2020, Dynamo models of the solar cycle.Living Reviews in Solar Physics 17,

    2020

  6. [6]

    DOI. ADS. Chen, J., Liu, Y., Wang, Z., Wang, C.: 2019, The Promotion Effect of LOESS Smoothing Technique in Short-term Traffic Volume Clustering. In:Proceedings of the 2019 Inter- national Conference on Modeling, Analysis, Simulation Technologies and Applications (MASTA 2019), Atlantis Press,

    2019

  7. [7]

    ISBN 978-94-6252-761-4. DOI. https://doi.org/10. 2991/masta-19.2019.65. Christensen-Dalsgaard, J., Berthomieu, G.: 1991, Theory of solar oscillations. In: Cox, A.N., Livingston, W.C., Matthews, M.S. (eds.)Solar Interior and Atmosphere,

    2019

  8. [8]

    Clette, F., Lef` evre, L.: 2015,SILSO Sunspot Number V2.0, https://doi.org/10.24414/qnza- ac80

    ADS. Clette, F., Lef` evre, L.: 2015,SILSO Sunspot Number V2.0, https://doi.org/10.24414/qnza- ac80. Published by WDC SILSO - Royal Observatory of Belgium (ROB). DOI. Covington, A.E.: 1947, Micro-Wave Solar Noise Observations During the Partial Eclipse of November 23, 1946.Nature159,

    work page doi:10.24414/qnza- 2015

  9. [9]

    DOI. ADS. Covington, A.E.: 1969, Solar Radio Emission at 10.7 cm, 1947-1968.J. R. Astron. Soc. Can. 63,

    1969

  10. [10]

    Elsworth, Y., Howe, R., Isaak, G.R., McLeod, C.P., New, R.: 1990, Variation of low-order acoustic solar oscillations over the solar cycle.Nature345,

    ADS. Elsworth, Y., Howe, R., Isaak, G.R., McLeod, C.P., New, R.: 1990, Variation of low-order acoustic solar oscillations over the solar cycle.Nature345,

    1990

  11. [11]

    DOI. ADS. Fletcher, S.T., Broomhall, A.-M., Salabert, D., Basu, S., Chaplin, W.J., Elsworth, Y., Garcia, R.A., New, R.: 2010, A Seismic Signature of a Second Dynamo?Astrophys. J. Lett.718, L19. DOI. ADS. Goldreich, P., Murray, N., Willette, G., Kumar, P.: 1991, Implications of Solar p-Mode Frequency Shifts.Astrophys. J.370,

    2010

  12. [12]

    DOI. ADS. Gonz´ alez Hern´ andez, I., Komm, R., Pevtsov, A., Leibacher, J.: 2014, Solar Origins of Space Weather and Space Climate: Preface.Sol. Phys.289,

    2014

  13. [13]

    DOI. ADS. Hajra, R., Marques de Souza Franco, A., Echer, E., Jos´ e Alves Bolzan, M.: 2021, Long Term Variations of the Geomagnetic Activity: A Comparison Between the Strong and Weak Solar Activity Cycles and Implications for the Space Climate.Journal of Geophysical Research (Space Physics)126, e28695. DOI. ADS. Harvey, J.W., Hill, F., Hubbard, R.P., Kenn...

    2021

  14. [14]

    DOI. ADS. Howard, R., Labonte, B.J.: 1980, The sun is observed to be a torsional oscillator with a period of 11 years.Astrophys. J. Lett.239, L33. DOI. ADS. Howe, R., Hill, F., Komm, R., Chaplin, W.J., Elsworth, Y., Davies, G.R., Schou, J., Thompson, M.J.: 2018, Signatures of Solar Cycle 25 in Subsurface Zonal Flows.Astrophys. J. Lett.862, L5. DOI. ADS. J...

    1980

  15. [15]

    DOI. ADS. Jain, K., Tripathy, S.C., Hill, F.: 2009, Solar Activity Phases and Intermediate-Degree Mode Frequencies.Astrophys. J.695,

    2009

  16. [16]

    DOI. ADS. SOLA: main.tex; 23 April 2026; 1:16; p. 17 Jain, Kumar and Tripathy Jain, K., Jain, N., Tripathy, S.C., Dikpati, M.: 2022, What Seismic Minimum Reveals about Solar Magnetism below the Surface.Astrophys. J. Lett.924, L20. DOI. ADS. Jain, R., Roberts, B.: 1993, Do p-Mode Frequency Shifts Suggest a Hotter Chromosphere at Solar Maximum?Astrophys. J.414,

    2026

  17. [17]

    DOI. ADS. Jain, R., Roberts, B.: 1996, Discrete High-Frequency p-Modes.Astrophys. J.456,

    1996

  18. [18]

    DOI. ADS. Kehinde, O.J., Ayinde, K., Lukman, A.F.: 2020, A hybrid model of LOESS and ARIMA for improved time series forecasting.Journal of Applied Statistics47,

    2020

  19. [19]

    Phys.293,

    Kiefer, R., Komm, R., Hill, F., Broomhall, A.-M., Roth, M.: 2018, GONG p-Mode Parameters Through Two Solar Cycles.Sol. Phys.293,

    2018

  20. [20]

    DOI. ADS. Kosovichev, A.G., Pipin, V.V.: 2019, Dynamo Wave Patterns inside of the Sun Revealed by Torsional Oscillations.Astrophys. J. Lett.871, L20. DOI. ADS. Larson, T.P., Schou, J.: 2018, Global-Mode Analysis of Full-Disk Data from the Michelson Doppler Imager and the Helioseismic and Magnetic Imager.Sol. Phys.293,

    2019

  21. [21]

    DOI. ADS. Leighton, R.B., Noyes, R.W., Simon, G.W.: 1962, Velocity Fields in the Solar Atmosphere. I. Preliminary Report.Astrophys. J.135,

    1962

  22. [22]

    DOI. ADS. Libbrecht, K.G., Woodard, M.F.: 1990, Solar-cycle effects on solar oscillation frequencies. Nature345,

    1990

  23. [23]

    DOI. ADS. Mandal, K., Kosovichev, A.G., Pipin, V.V.: 2024, Helioseismic Properties of Dynamo Waves in the Variation of Solar Differential Rotation.Astrophys. J.973,

    2024

  24. [24]

    DOI. ADS. Mehta, T., Jain, K., Tripathy, S.C., Kiefer, R., Kolotkov, D., Broomhall, A.-M.: 2022, Cycle dependence of a quasi-biennial variability in the solar interior.Mon. Not. R. Astron. Soc. 515,

    2022

  25. [25]

    DOI. ADS. Mursula, K., Usoskin, I.G., Maris, G.: 2007, Introduction to Space Climate.Advances in Space Research40,

    2007

  26. [26]

    DOI. ADS. Oreshkin, B.N., Carpov, D., Chapados, N., Bengio, Y.: 2019, N-BEATS: Neural basis expansion analysis for interpretable time series forecasting.arXiv e-prints, arXiv:1905.10437. DOI. ADS. Rabello Soares, M.C.: 2019, On the saturation of acoustic mode frequencies at high solar activity.Mon. Not. R. Astron. Soc.486,

    work page arXiv 2019

  27. [27]

    DOI. ADS. Rabello-Soares, M.C., Korzennik, S.G., Schou, J.: 2006, High-degree mode frequencies: changes with solar cycle. In: Fletcher, K., Thompson, M. (eds.)Proceedings of SOHO 18/GONG 2006/HELAS I, Beyond the spherical Sun,ESA Special Publication624,

    2006

  28. [28]

    Rhodes, E.J., Cacciani, A., Korzennik, S.G.: 1991, Observations of intermediate- and high- degree p-mode oscillations during sunspot cycles 21 and 22.Advances in Space Research 11,

    ADS. Rhodes, E.J., Cacciani, A., Korzennik, S.G.: 1991, Observations of intermediate- and high- degree p-mode oscillations during sunspot cycles 21 and 22.Advances in Space Research 11,

    1991

  29. [29]

    DOI. ADS. Rhodes, E.J. Jr., Reiter, J., Schou, J.: 2002, Solar cycle variability of high-frequency and high- degree p-mode oscillation frequencies. In: Wilson, A. (ed.)From Solar Min to Max: Half a Solar Cycle with SOHO,ESA Special Publication508,

    2002

  30. [30]

    Salabert, D., Fossat, E., Gelly, B., Kholikov, S., Grec, G., Lazrek, M., Schmider, F.X.: 2004, Solar p modes in 10 years of the IRIS network.Astron

    ADS. Salabert, D., Fossat, E., Gelly, B., Kholikov, S., Grec, G., Lazrek, M., Schmider, F.X.: 2004, Solar p modes in 10 years of the IRIS network.Astron. Astrophys.413,

    2004

  31. [31]

    Shao, Z., Chao, F., Yang, S.-L., Zhou, K.-L.: 2017, A review of the decomposition method- ology for extracting and identifying the fluctuation characteristics in electricity demand forecasting.Renew. Sustain. Energy Rev.75,

    2017

  32. [32]

    Su, X., Liang, B., Feng, S., Dai, W., Yang, Y.: 2023, Solar Cycle 25 Prediction Using N-BEATS

    DOI. Su, X., Liang, B., Feng, S., Dai, W., Yang, Y.: 2023, Solar Cycle 25 Prediction Using N-BEATS. Astrophys. J.947,

    2023

  33. [33]

    DOI. ADS. Tapping, K.F.: 2013, The 10.7 cm solar radio flux (F10.7).Space Weather11,

    2013

  34. [34]

    DOI. ADS. Tripathy, S.C., Hill, F., Jain, K., Leibacher, J.W.: 2007, Solar Oscillation Frequency Changes on Time Scales of Nine Days.Sol. Phys.243,

    2007

  35. [35]

    DOI. ADS. Ulrich, R.K.: 1970, The Five-Minute Oscillations on the Solar Surface.Astrophys. J.162,

    1970

  36. [36]

    DOI. ADS. Wasilewski, F.: 2012,PyWavelets Documentation, https://pywavelets.readthedocs.io/ /downloads/en/0.2.0/pdf/#:∼:text=decomposition%20using%20wavedec-,pywt. Accessed: 2026-02-05. Woodard, M.F., Noyes, R.W.: 1985, Change of solar oscillation eigenfrequencies with the solar cycle.Nature318,

    2012

  37. [37]

    DOI. ADS. Woodard, M.F., Kuhn, J.R., Murray, N., Libbrecht, K.G.: 1991, Short-Term Changes in Solar Oscillation Frequencies and Solar Activity.Astrophys. J. Lett.373, L81. DOI. ADS. SOLA: main.tex; 23 April 2026; 1:16; p. 18 Machine Learning–Based Characterization of Solar p-Mode Frequency Shifts Xu, Q., Jain, R., Xing, W.: 2024, Data-Driven Forecasting o...

    1991

  38. [38]

    DOI. ADS. Yuan, F., Fan, Y., Bing, X., Tian, C., Yuan, Z., Li, Y.: 2025, A Decomposition-Driven Hybrid Framework Based on STL for Accurate Traffic Flow Forecasting.Renew. Sustain. Energy Rev.xx, x. DOI. Zhang, X., Li, R.: 2021, A Novel Decomposition and Combination Technique for Forecasting Monthly Electricity Consumption.Frontiers in Energy Research9, 79...

    2025