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Deep Neural Network Driven Simulation Based Inference Method for Pole Position Estimation under Model Misspecification

T0 review · 2 major / 6 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Simulation-based inference yields more accurate rho(770) pole positions than chi-squared minimization under model misspecification.

desk verdict A credible SBI-vs-chi2 proof-of-concept whose real-data claim is weakened by a chi2-anchored training filter that the authors underplay. read the letter →

arxiv 2507.18824 v2 pith:NDR7PZ7L submitted 2025-07-24 hep-ph nucl-thstat.APstat.ML

Daniel Sadasivan , Isaac Cordero , Andrew Graham , Cecilia Marsh , Daniel Kupcho , Melana Mourad , Maxim Mai This is my paper · ORCID
classification hep-phnucl-thstat.APstat.ML
keywords simulationbasedinferencemodelmisspecificationresonancepolepositionrho(770)pi-piscatteringneuralnetworkK-matrixchi-squaredminimization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that when the model being fitted does not actually describe the data, a neural-network-based Simulation Based Inference (SBI) pipeline can estimate the rho(770) resonance pole more accurately than traditional chi-squared minimization. The demonstration starts with two toy models—one with intentionally corrupted points and one with non-Gaussian noise—where the true parameters are known, and then moves to actual pi-pi scattering phase-shift data fitted with a K-matrix amplitude using two and three subtractions. In all four model-and-data combinations, the SBI pole position is as close as or closer to reference values than the pole from chi-squared minimization, even though the chi-squared curve sits closer to the data points themselves. The broader reason to care is that many hadron spectroscopy analyses rely on data with documented ambiguities, so a method that resists misspecification could change how resonance parameters are extracted. The paper explicitly limits its claim: in near-ideal settings chi-squared minimization remains the better approach.

What carries the argument

The central mechanism is the SBI training pipeline: sample $10^6$ random K-matrix parameters from broad priors, generate Gaussian pseudodata at the experimental energy points with the same uncertainties as the real data, keep only pseudodata whose fitted pole falls inside a square centered on the chi-squared pole from the actual data, and train a four-hidden-layer neural network to predict the generating parameters from the pseudodata curves. The training is repeated $N=100$ times and the average prediction is quoted with uncertainty $\sigma/\sqrt{N}$. The physical object being estimated is the resonance pole $E^* = M - i\Gamma/2$ obtained by analytic continuation of the K-matrix amplitude with $n$ subtractions. The comparison baseline is standard chi-squared minimization with bootstrap uncertainties on the same models and data.

What would settle it

Retrain the SBI network with the retention window centered on a different point—for example, on the reference pole instead of the chi-squared pole—and compare the predicted pole position. If the prediction follows the center, the reported advantage is an anchoring artifact; if it does not move, the advantage is robust. The same comparison across several independent data sets would quantify how general the claim is.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is a proof of concept: under model misspecification, SBI delivers resonance parameters closer to the true or reference values than chi-squared minimization does. In the toy examples, the SBI mass and width are far closer to the generating values, especially the width in the outlier example. In the real-data application, four combinations of two data sets and two subtraction numbers are considered, and in every case the SBI pole $E^* = M - i\Gamma/2$ lies closer to the reference values than the chi-squared pole; for the three-subtraction combined fit the data show clear misspecification ($\chi^2/\mathrm{dof}=3.1$, $p=0.17\times10^{-3}$), yet SBI still lands closer to the reference values. The paper interprets SBI as an approximate Bayesian inference in which the random parameter draw serves as a prior and the pseudodata encode the likelihood, so the network approximates $P(\vec a \mid \vec y)$ rather than the single best-fitting curve.

Load-bearing premise

The load-bearing premise is that restricting the SBI training set to pseudodata whose fitted poles lie in a square centered on the chi-squared pole does not itself move the network's prediction toward the SBI answer; the paper's own check shows the average training pole is closer to the SBI result than to the chi-squared result in the two-subtraction cases, so the premise is only partially supported.

Editorial extensions

If this is right

  • Because SBI does not need to identify which data points are flawed, it can be used when the source of misspecification is unknown, as long as pseudodata can be generated from a candidate model.
  • The classifier part of the pipeline can pick the most probable model (here, three subtractions) from pseudodata before the final parameter extraction, so model choice and parameter estimation can be joined in one workflow.
  • The same pipeline transfers to other resonances whose data are ambiguous, such as the $a_1(1260)$ and $\omega(782)$ cases mentioned in the paper, without changing the core procedure.
  • In near-ideal fits the chi-squared method is still expected to be better, so SBI is a complementary tool for misspecified data rather than a replacement for standard practice.
  • The combined three-subtraction SBI fit provides a candidate set of $\rho(770)$ pole parameters closer to reference values than the corresponding chi-squared fit, which matters for downstream analyses that use $\pi\pi$ scattering input.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A decisive test beyond the paper would be to rerun the training with the pole-retention window centered on the reference pole instead of the chi-squared pole; if the SBI answer moves with the window, part of the reported advantage is an artifact.
  • The same procedure could be tried on resonances with notoriously inconsistent data, such as the $\Lambda(1405)$ two-pole structure, where the underlying model uncertainty is larger than here.
  • If the advantage survives de-anchoring, one practical consequence is that legacy resonance parameters extracted by chi-squared fits from old data sets may need rechecking with misspecification-robust methods.
  • The dependence of SBI on the chosen parameter prior ranges can be measured directly by widening or shifting the uniform priors and observing how the final pole prediction changes.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. The paper proposes the use of neural-network-based Simulation Based Inference (SBI) as an alternative to chi-squared minimization for extracting resonance pole positions when the fitted model is misspecified. The method is first demonstrated on two toy models with known ground truth, where SBI is claimed to recover the generating parameters substantially better than chi2 minimization. The method is then applied to pi-pi scattering phase-shift data from two experiments (Protopopescu and Estabrooks) using two K-matrix models with two and three subtractions, giving four real-data cases. In all four cases the SBI pole is reported to be closer to the PDG reference values than the chi2 pole. A classifier network is also used to select the number of subtractions, and a combined fit is performed. The paper includes appendices documenting tests of the neural network architecture and of the convergence of the reported uncertainties.

Significance. If the central claim is correct, the paper provides a useful proof of concept that SBI can be more robust than chi2 minimization under model misspecification, with direct relevance to hadron spectroscopy where data ambiguities are common. The paper is clearly written and gives a reproducible description of the pipeline, including the pseudodata generation, the neural-network architecture, and empirical checks in Appendices A and B. The toy examples are valuable because the ground truth is known and the observed differences between SBI and chi2 are large. However, the real-data claim is currently confounded by a data-dependent training filter whose influence is only partially quantified, and the comparison to PDG values is not accompanied by a statistical test of significance. These issues affect the load-bearing conclusion of the paper and need to be addressed before the claim can be accepted.

major comments (2)
  1. [Sec. III C, Table III] The chi2-anchored retention window is a data-dependent prior that can bias the SBI prediction toward the training distribution. The paper's own Table III shows that for the two n=2 cases, the average training pole is closer to the SBI pole than to the chi2 pole: 9.1 vs 13.2 MeV for Estabrooks and 8.3 vs 10.6 MeV for Protopopescu, whereas the SBI-to-chi2 distances are 18.5 and 9.5 MeV, respectively. The text in Sec. III C states that the average training pole is "roughly equidistant" from the two methods, but the differences are 4.1 and 2.3 MeV, which are 22% and 24% of the corresponding SBI-chi2 separations. This is not negligible, and it is exactly in the direction of the claimed SBI advantage. The statement in Sec. III C that the retention step "ensures that, if the SBI method makes a more accurate prediction than the chi2 method, it is not because it is trained on data that is closer to known position" is therefore misleading: the training distribution is closer to the SBI prediction than to the chi2 prediction. A sensitivity analysis with retention windows centered on a range of positions spanning the chi2 and SBI poles, or an otherwise reweighted prior, is needed to establish that the n=2 real-data results are not an artifact of the filter.
  2. [Sec. II B and Sec. III A] The claim that SBI is "more accurate" or "as close or closer" is based on point estimates without a statistical measure of the difference. The toy examples in Sec. II B are single realizations; no repeated-experiment or coverage analysis is reported that would show how often SBI beats chi2 across random draws of the misspecified data. For the real-data cases, the differences between SBI and chi2 are sometimes comparable to the reported one-sigma uncertainties. For instance, in the Estabrooks n=3 case of Table II the real parts differ by 769.6 - 766.8 = 2.8 MeV, while the SBI uncertainty on that quantity is 2.9 MeV. A bootstrap of the difference, or a paired test over the N=100 network realizations, should be reported before the conclusion of a systematically more accurate method is drawn.
minor comments (6)
  1. [Abstract] The sentence "SBI is shown to make a more robust predictions" is ungrammatical; it should read "SBI is shown to make more robust predictions" or "a more robust prediction".
  2. [Sec. II B, text after Table I] The text states that the SBI width is closer to the true value "by more than an order of magnitude" than the chi2 width. From Table I, the distance to the true value is 174.5 MeV for SBI (293.5 vs 119.0) and 363.6 MeV for chi2 (482.6 vs 119.0), a factor of about 2.1. This statement should be corrected or substantiated.
  3. [Sec. III C] "The training data is given to a neural network" should be "The training data are given", since "data" is plural.
  4. [Fig. 1] The caption refers to "boxes" but the figure is a flow diagram; the boxes in the middle and bottom rows are not clearly labeled in the text. Please add labels or refer to the components explicitly in the caption.
  5. [Eq. (4)] The uncertainty notation "0.06482(00095)" is nonstandard and confusing; use "0.06482(95)" or "0.06482 \pm 0.00095".
  6. [Table II] The SBI columns list the fitted K-matrix parameters a_i without uncertainties, while the pole-position uncertainties are derived from the spread of the N network outputs. Reporting the parameter uncertainties would aid reproducibility and comparison with the chi2 results.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the SBI predictions are not constructed from the chi2 results or PDG reference values, and the one data-anchoring concern is explicitly acknowledged and tested.

full rationale

The derivation chain is self-contained in the relevant sense. The SBI training labels are randomly sampled model parameters (Sec. II A 1), not the PDG pole positions or the chi2 pole positions, so the comparison against PDG values in Table II is an external benchmark rather than a fitted target. The chi2-anchored retention window in Sec. III C is the only step that uses the chi2 result to shape the training distribution; however, the SBI output is not the center of that window (e.g., for Estabrooks n=2 the window is centered on the chi2 pole 750.3-i69.8 and the SBI result is 766.3-i79.0, while the average retained training pole is 757.4-i80.8), so the prediction is not forced by construction. The paper explicitly quantifies the possible bias in Table III and shows the average training pole is roughly equidistant from both methods, and the n=3 cases show the training pole far from both predictions. No load-bearing result is imported solely from a self-citation: Eq. (3) is a standard K-matrix parametrization cited to the authors' prior work but used as a model, not as a uniqueness theorem or as a substitute for the numerical comparison. Toy examples provide controlled tests with known generating parameters. Therefore no step reduces to its own inputs.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central comparison rests on the simulated likelihood being Gaussian, on the K-matrix model being an adequate representation, on the PDG pole values being a valid reference, and on the training-data filter not biasing the result. No new particles, forces, or entities are introduced.

free parameters (5)
  • Toy prior range for mass M = uniform [400,1200] MeV
    Chosen by hand in Sec II B; defines the training distribution for the toy SBI model.
  • Toy prior range for width Gamma = uniform [0,500] MeV
    Chosen by hand in Sec II B; together with the M prior sets the reachable pole region.
  • K-matrix parameter priors a0,a1,a2 = uniform: a0 in [-GeV^2/M_pi^2, GeV^2/M_pi^2], a1 in [-1,1], a2 in [-M_pi^2/GeV^2, M_pi^2/GeV^2]
    Chosen in Sec III C; these ranges determine the distribution of physical poles in the SBI training set.
  • Pole retention window around chi2 pole = square with half-width b in Re E*, height 2b in Im E* below the real axis
    Sec III C filter that anchors training pseudodata to the chi2 pole and can bias the SBI comparison.
  • Neural network architecture and optimizer = 4 hidden layers (40,30,20,10), relu and leaky_relu, MSE loss, Adam, batch size 2000, early stopping
    Selected somewhat arbitrarily in Sec II B; Appendix A shows stability with size, but the choice remains an input to the method.
assumptions (5)
  • domain assumption Gaussian noise in pseudodata generation
    Sec II A Step 2: y_p = R(f(x_i), sigma_i) with a normal distribution. This is the likelihood assumed for SBI training and chi2; in toy example 2 the true noise is non-Gaussian, creating the misspecification.
  • domain assumption K-matrix model with n subtractions describes pi-pi scattering in the rho region
    Sec III Eq (3): pole positions are extracted from this model, and results change with n, so the adequacy of the model family is assumed.
  • domain assumption PDG reference pole values are a valid accuracy benchmark
    Sec III A and Fig 3: 'closer to reference values' is used as 'more accurate' for real data; PDG values are themselves fit results from other experiments and carry their own modeling assumptions.
  • domain assumption The two selected data sets are the correct testbed and contain misspecification
    Sec III: chi2/dof = 3.1 for the combined n=3 fit is used to infer misspecification; the choice of Protopopescu and Estabrooks data frames the comparison.
  • ad hoc to paper Classifier model family n=1..5 subtractions is exhaustive
    Sec III B: the classifier computes P(n) only over K-matrix models with 1 to 5 subtractions and assumes the actual data were generated by one of these models; this exhaustiveness is untested.

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Cite this review

Pith. "Pith review of Deep Neural Network Driven Simulation Based Inference Method for Pole Position Estimation under Model Misspecification." pith.science (2026). https://pith.science/paper/NDR7PZ7L

@misc{pith2026250718824,
  author       = {Pith},
  title        = {Pith review of: Deep Neural Network Driven Simulation Based Inference Method for Pole Position Estimation under Model Misspecification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NDR7PZ7L}},
  note         = {Machine review of arXiv:2507.18824}
}
read the original abstract

Simulation Based Inference (SBI) is shown to yield more accurate resonance parameter estimates than traditional chi-squared minimization in certain cases of model misspecification, demonstrated through a case study of pi-pi scattering and the rho(770) resonance. Models fit to some data sets using chi-squared minimization can predict inaccurate pole positions for the rho(770), while SBI provides more robust predictions across the same models and data. This result is significant both as a proof of concept that SBI can handle model misspecification, and because accurate modeling of pi-pi scattering is essential in the study of many contemporary physical systems (e.g., a1(1260), omega(782)). The method of Simulation Based Inference is shown to lead to a more accurate resonance parameter estimation than traditional chi-squared minimization in certain cases of model misspecification in a case-study of pi-pi scattering and the rho(770)-resonance. Models fit to certain data sets using chi-squared minimization can make inaccurate predictions for the pole position of the rho(770). SBI is shown to make a more robust predictions for the pole positions. This is significant, both as a proof of concept that the SBI method can be used in cases of model misspecification, and because models of pi-pi scattering are a crucial part to many physical systems of contemporary interest (e.g., a1(1260), omega(782)).

Figures

Figures reproduced from arXiv: 2507.18824 by the authors.

Figure 1
Figure 1. FIG. 1. A diagrammatic depiction of the data pipeline in the SBI method employed in this work. In each of the boxes on the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Left: Phase-shift data with two points that are intentionally modified to create a case of extreme model misspecification [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The pole position confidence regions of the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Left: A comparison of the SBI method (blue) and the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

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    ρandK∗ resonances on the lattice at nearly physical quark masses andN f = 2,

    Gunnar S. Bali, Sara Collins, Antonio Cox, Gordon Donald, Meinulf G¨ ockeler, C. B. Lang, and Andreas Sch¨ afer (RQCD), “ρandK∗ resonances on the lattice at nearly physical quark masses andN f = 2,” Phys. Rev. D93, 054509 (2016), arXiv:1512.08678 [hep-lat]

    2016 arXiv

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    Coupledππ,K ¯Kscattering inP-wave and theρ resonance from lattice QCD,

    David J. Wilson, Raul A. Briceno, Jozef J. Dudek, Robert G. Edwards, and Christopher E. Thomas, “Coupledππ,K ¯Kscattering inP-wave and theρ resonance from lattice QCD,” Phys. Rev. D92, 094502 (2015), arXiv:1507.02599 [hep-ph]

    2015 arXiv

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    Studying theρresonance parameters with staggered fermions,

    Ziwen Fu and Lingyun Wang, “Studying theρresonance parameters with staggered fermions,” Phys. Rev. D94, 034505 (2016), arXiv:1608.07478 [hep-lat]

    2016 arXiv

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    Universal parameters of the Λ(1380), the Λ(1405) and their isospin partners from a combined analysis of Lattice QCD and experimental results,

    Ferenc Pittler, Maxim Mai, Ulf-G. Meißner, Ryan F. Ferguson, Peter Hurck, David G. Ireland, and Bryan McKinnon, “Universal parameters of the Λ(1380), the Λ(1405) and their isospin partners from a combined analysis of Lattice QCD and experimental results,” (2025), arXiv:2507.14...

    2025 arXiv

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    2019 arXiv

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    Hadron-Hadron Interactions fromN f = 2 + 1 + 1 Lattice QCD: Theρ-resonance,

    Markus Werneret al.(Extended Twisted Mass), “Hadron-Hadron Interactions fromN f = 2 + 1 + 1 Lattice QCD: Theρ-resonance,” Eur. Phys. J. A56, 61 (2020), arXiv:1907.01237 [hep-lat]

    2020 arXiv

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    Extraction of isoscalar ππphase-shifts from lattice QCD,

    Dehua Guo, Andrei Alexandru, Raquel Molina, Maxim Mai, and Michael D¨ oring, “Extraction of isoscalar ππphase-shifts from lattice QCD,” Phys. Rev. D98, 014507 (2018), arXiv:1803.02897 [hep-lat]

    2018 arXiv

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    Chiral extrapolations of theρ(770) meson inN f =2+1lattice QCD simulations,

    B. Hu, R. Molina, M. D¨ oring, M. Mai, and A. Alexandru, “Chiral extrapolations of theρ(770) meson inN f =2+1lattice QCD simulations,” Phys. Rev. D96, 034520 (2017), arXiv:1704.06248 [hep-lat]

    2017 arXiv

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    Two-flavor simulations of theρ(770) and the role of theK Kchannel,

    Bin Hu, Raquel Molina, Michael Doring, Andrei Alexandru, and Dehua Guo, “Two-flavor simulations of theρ(770) and the role of theK Kchannel,” PoS LATTICE2016, 096 (2016)

    2016

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    Rho resonance parameters from lattice QCD,

    Dehua Guo, Andrei Alexandru, Raquel Molina, and Michael D¨ oring, “Rho resonance parameters from lattice QCD,” Phys. Rev. D94, 034501 (2016), arXiv:1605.03993 [hep-lat]

    2016 arXiv

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    Theρ-resonance from Nf=2 lattice QCD including the physical pion mass,

    Matthias Fischer, Bartosz Kostrzewa, Maxim Mai, Marcus Petschlies, Ferenc Pittler, Martin Ueding, Carsten Urbach, and Markus Werner (Extended Twisted Mass, ETM), “Theρ-resonance from Nf=2 lattice QCD including the physical pion mass,” Phys. Lett. B819, 136449 (2021), arXiv:200...

    2021 arXiv

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    Bayesian Analysis and Analytic Continuation of Scattering Amplitudes from Lattice QCD,

    Miguel Salg, Fernando Romero-L´ opez, and William I. Jay, “Bayesian Analysis and Analytic Continuation of Scattering Amplitudes from Lattice QCD,” (2025), arXiv:2506.16161 [hep-lat]

    2025

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    S- and p-wave structure ofS=−1 meson-baryon scattering in the resonance region,

    D. Sadasivan, M. Mai, and M. D¨ oring, “S- and p-wave structure ofS=−1 meson-baryon scattering in the resonance region,” Phys. Lett. B789, 329–335 (2019), arXiv:1805.04534 [nucl-th]

    2019 arXiv

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    Three-body resonances in theφ 4 theory,

    Marco Garofalo, Maxim Mai, Fernando Romero-L´ opez, Akaki Rusetsky, and Carsten Urbach, “Three-body resonances in theφ 4 theory,” JHEP02, 252 (2023), arXiv:2211.05605 [hep-lat]

    2023 arXiv

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    Review of the Λ(1405) A curious case of a strangeness resonance,

    Maxim Mai, “Review of the Λ(1405) A curious case of a strangeness resonance,” Eur. Phys. J. ST230, 1593– 1607 (2021), arXiv:2010.00056 [nucl-th]

    2021 arXiv

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    J¨ ulich-Bonn-Washington model for pion electroproduction multipoles,

    Maxim Mai, Michael D¨ oring, Carlos Granados, Helmut Haberzettl, Ulf-G. Meißner, Deborah R¨ onchen, Igor Strakovsky, and Ron Workman (J¨ ulich-Bonn- Washington), “J¨ ulich-Bonn-Washington model for pion electroproduction multipoles,” Phys. Rev. C103, 065204 (2021), arXiv:2104....

    2021 arXiv

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    Three-body Unitarity with Isobars Revisited,

    M. Mai, B. Hu, M. Doring, A. Pilloni, and A. Szczepaniak, “Three-body Unitarity with Isobars Revisited,” Eur. Phys. J. A53, 177 (2017), arXiv:1706.06118 [nucl-th]

    2017 arXiv

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    Dalitz plots and lineshape ofa 1(1260) from a relativistic three-body unitary approach,

    D. Sadasivan, M. Mai, H. Akdag, and M. D¨ oring, “Dalitz plots and lineshape ofa 1(1260) from a relativistic three-body unitary approach,” Phys. Rev. D 101, 094018 (2020), [Erratum: Phys.Rev.D 103, 019901 (2021)], arXiv:2002.12431 [nucl-th]

    2020 arXiv

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    Pole position of the a1(1260) resonance in a three-body unitary framework,

    Daniel Sadasivan, Andrei Alexandru, Hakan Akdag, Felipe Amorim, Ruair´ ı Brett, Chris Culver, Michael D¨ oring, Frank X. Lee, and Maxim Mai, “Pole position of the a1(1260) resonance in a three-body unitary framework,” Phys. Rev. D105, 054020 (2022), arXiv:2112.03355 [hep-ph]

    2022 arXiv

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    Three-Body Dynamics of the a1(1260) Resonance from Lattice QCD,

    Maxim Mai, Andrei Alexandru, Ruair´ ı Brett, Chris Culver, Michael D¨ oring, Frank X. Lee, and Daniel Sadasivan (GWQCD), “Three-Body Dynamics of the a1(1260) Resonance from Lattice QCD,” Phys. Rev. Lett.127, 222001 (2021), arXiv:2107.03973 [hep-lat]

    2021 arXiv

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    A unitary coupled-channel three-body amplitude with pions and kaons,

    Yuchuan Feng, Fernando Gil, Michael D¨ oring, Raquel Molina, Maxim Mai, Vanamali Shastry, and Adam Szczepaniak, “A unitary coupled-channel three-body amplitude with pions and kaons,” Phys. Rev. D110, 094002 (2024), arXiv:2407.08721 [nucl-th]

    2024 arXiv

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    ωMeson from Lattice QCD,

    Haobo Yan, Maxim Mai, Marco Garofalo, Ulf-G. Meißner, Chuan Liu, Liuming Liu, and Carsten Urbach, “ωMeson from Lattice QCD,” Phys. Rev. Lett.133, 211906 (2024), arXiv:2407.16659 [hep-lat]

    2024 arXiv

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    Dynamical coupled-channel models for hadron dynamics,

    Michael D¨ oring, Johann Haidenbauer, Maxim Mai, and Toru Sato, “Dynamical coupled-channel models for hadron dynamics,” (2025), arXiv:2505.02745 [nucl-th]

    2025

  51. [59]

    Three-body scattering in isobar ansatz,

    Maxim Mai, Bin Hu, Michael Doring, Alessandro Pilloni, and Adam Szczepaniak, “Three-body scattering in isobar ansatz,” PoSHadron2017, 140 (2018)

    2018

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    Multi-particle systems on the lattice and chiral extrapolations: a brief review,

    Maxim Mai, Michael D¨ oring, and Akaki Rusetsky, “Multi-particle systems on the lattice and chiral extrapolations: a brief review,” Eur. Phys. J. ST230, 1623–1643 (2021), arXiv:2103.00577 [hep-lat]

    2021 arXiv

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    Finite-volume energy spectrum of the K−K−K− system,

    Andrei Alexandru, Ruair´ ı Brett, Chris Culver, Michael D¨ oring, Dehua Guo, Frank X. Lee, and Maxim Mai, “Finite-volume energy spectrum of the K−K−K− system,” Phys. Rev. D102, 114523 (2020), arXiv:2009.12358 [hep-lat]

    2020 arXiv

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    Three pion spectrum in theI= 3 channel from lattice QCD,

    Chris Culver, Maxim Mai, Ruair´ ı Brett, Andrei Alexandru, and Michael D¨ oring, “Three pion spectrum in theI= 3 channel from lattice QCD,” Phys. Rev. D 101, 114507 (2020), arXiv:1911.09047 [hep-lat]

    2020 arXiv

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    Three-body unitarity versus finite-volumeπ +π+π+ spectrum from lattice QCD,

    M. Mai, M. D¨ oring, C. Culver, and A. Alexandru, “Three-body unitarity versus finite-volumeπ +π+π+ spectrum from lattice QCD,” Phys. Rev. D101, 054510 (2020), arXiv:1909.05749 [hep-lat]

    2020 arXiv

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    Cross-channel study of pion scattering from lattice QCD,

    Maxim Mai, Chris Culver, Andrei Alexandru, Michael D¨ oring, and Frank X. Lee, “Cross-channel study of pion scattering from lattice QCD,” Phys. Rev. D100, 114514 (2019), arXiv:1908.01847 [hep-lat]

    2019 arXiv

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    Pion scattering in the isospinI= 2 channel from elongated lattices,

    C. Culver, M. Mai, A. Alexandru, M. D¨ oring, and F. X. Lee, “Pion scattering in the isospinI= 2 channel from elongated lattices,” Phys. Rev. D100, 034509 (2019), arXiv:1905.10202 [hep-lat]

    2019 arXiv

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    3-body quantization condition in unitary isobar formalism,

    Maxim Mai, “3-body quantization condition in unitary isobar formalism,” PoSLATTICE2018, 050 (2018), arXiv:1810.00604 [hep-lat]

    2018 arXiv

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    Finite-Volume Spectrum ofπ +π+ andπ +π+π+ Systems,

    Maxim Mai and Michael Doring, “Finite-Volume Spectrum ofπ +π+ andπ +π+π+ Systems,” Phys. Rev. Lett.122, 062503 (2019), arXiv:1807.04746 [hep-lat]

    2019 arXiv

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    Three-body spectrum in a finite volume: the role of cubic symmetry,

    M. D¨ oring, H. W. Hammer, M. Mai, J. Y. Pang,§A. Rusetsky, and J. Wu, “Three-body spectrum in a finite volume: the role of cubic symmetry,” Phys. Rev. D97, 114508 (2018), arXiv:1802.03362 [hep-lat]

    2018 arXiv

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    Line shape analysis of Λ(1405) inγp→K +Σ−π+ reaction using convolutional neural network,

    Vince Angelo A. Chavez and Denny Lane B. Sombillo, “Line shape analysis of Λ(1405) inγp→K +Σ−π+ reaction using convolutional neural network,” in21st International Conference on Hadron Spectroscopy and Structure(2025) arXiv:2506.04622 [hep-ph]

    2025 arXiv

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    Three-body Unitarity in the Finite Volume,

    M. Mai and M. D¨ oring, “Three-body Unitarity in the Finite Volume,” Eur. Phys. J. A53, 240 (2017), arXiv:1709.08222 [hep-lat]

    2017 arXiv

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    Lattice model of heavy- 12 light three-body system,

    Peng Guo and Michael D¨ oring, “Lattice model of heavy- 12 light three-body system,” Phys. Rev. D101, 034501 (2020), arXiv:1910.08624 [hep-lat]

    2020 arXiv

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    Variational approach toN-body interactions in finite volume,

    Peng Guo, Michael D¨ oring, and Adam P. Szczepaniak, “Variational approach toN-body interactions in finite volume,” Phys. Rev. D98, 094502 (2018), arXiv:1810.01261 [hep-lat]

    2018 arXiv

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    Dalitz-plot decomposition for three-body decays,

    M. Mikhasenkoet al.(JPAC), “Dalitz-plot decomposition for three-body decays,” Phys. Rev. D101, 034033 (2020), arXiv:1910.04566 [hep-ph]

    2020 arXiv

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    Khuri- Treiman equations for 3πdecays of particles with spin,

    M. Albaladejo, D. Winney, I. V. Danilkin, C. Fern´ andez- Ram´ ırez, V. Mathieu, M. Mikhasenko, A. Pilloni, J. A. Silva-Castro, and A. P. Szczepaniak (JPAC), “Khuri- Treiman equations for 3πdecays of particles with spin,” Phys. Rev. D101, 054018 (2020), arXiv:1910.03107 [hep-ph]

    2020 arXiv

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    Three-body scattering: Ladders and Resonances,

    M. Mikhasenko, Y. Wunderlich, A. Jackura, V. Mathieu, A. Pilloni, B. Ketzer, and A. P. Szczepaniak, “Three-body scattering: Ladders and Resonances,” JHEP08, 080 (2019), arXiv:1904.11894 [hep-ph]

    2019 arXiv

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    Deep learning exotic hadrons,

    L. Ng, L. Bibrzycki, J. Nys, C. Fernandez-Ramirez, A. Pilloni, V. Mathieu, A. J. Rasmusson, and A. P. Szczepaniak (Joint Physics Analysis Center, JPAC), “Deep learning exotic hadrons,” Phys. Rev. D105, L091501 (2022), arXiv:2110.13742 [hep-ph]

    2022 arXiv

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    Machine learning exotic hadrons,

    L. Ng, L. Bibrzycki, J. Nys, C. Fern´ andez-Ram´ ırez, A. Pilloni, V. Mathieu, A. J. Rasmusson, and A. P. Szczepaniak, “Machine learning exotic hadrons,” Nuovo Cim. C47, 207 (2024)

    2024

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    Pole structure of PψN(4312)+ via machine learning and uniformized S-matrix,

    Leonarc Michelle Santos, Vince Angelo A. Chavez, and Denny Lane B. Sombillo, “Pole structure of PψN(4312)+ via machine learning and uniformized S-matrix,” J. Phys. G52, 015104 (2025), arXiv:2405.11906 [hep-ph]

    2025 arXiv

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    Classifying the pole of an amplitude using a deep neural network,

    Denny Lane B. Sombillo, Yoichi Ikeda, Toru Sato, and Atsushi Hosaka, “Classifying the pole of an amplitude using a deep neural network,” Phys. Rev. D102, 016024 (2020), arXiv:2003.10770 [hep-ph]

    2020 arXiv

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    Meson mass and width: Deep learning approach,

    M. Malekhosseini, S. Rostami, A. R. Olamaei, R. Ostovar, and K. Azizi, “Meson mass and width: Deep learning approach,” Phys. Rev. D110, 054011 (2024), arXiv:2404.00448 [hep-ph]

    2024 arXiv

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    Analysis of hidden-charm pentaquarks as triangle singularities via deep learning,

    Darwin Alexander O. Co and Denny Lane B. Sombillo, “Analysis of hidden-charm pentaquarks as triangle singularities via deep learning,” PoSQNP2024, 031 (2025), arXiv:2411.14044 [hep-ph]

    2025 arXiv

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    Reconstructing S-matrix Phases with Machine Learning,

    Aur´ elien Dersy, Matthew D. Schwartz, and Alexander Zhiboedov, “Reconstructing S-matrix Phases with Machine Learning,” JHEP05, 200 (2024), arXiv:2308.09451 [hep-th]

    2024 arXiv

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    Feature extraction in partial wave analysis usingK-matrix approach,

    Adam B. Mapa and Denny Lane B. Sombillo, “Feature extraction in partial wave analysis usingK-matrix approach,” in21st International Conference on Hadron Spectroscopy and Structure(2025) arXiv:2506.04628 [hep-ph]

    2025 arXiv

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    Deep learning framework for disentangling triangle singularity and pole-based enhancements,

    Darwin Alexander O. Co, Vince Angelo A. Chavez, and Denny Lane B. Sombillo, “Deep learning framework for disentangling triangle singularity and pole-based enhancements,” Phys. Rev. D110, 114034 (2024), arXiv:2403.18265 [hep-ph]

    2024 arXiv

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    Extraction of S-matrix pole structure using deep learning,

    Denny Lane Sombillo, “Extraction of S-matrix pole structure using deep learning,” PoSPANIC2021, 175 (2022)

    2022

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    Classifying Near-Threshold Enhancement Using Deep Neural Network,

    Denny Lane B. Sombillo, Yoichi Ikeda, Toru Sato, and Atsushi Hosaka, “Classifying Near-Threshold Enhancement Using Deep Neural Network,” Few Body Syst.62, 52 (2021), arXiv:2106.03453 [hep-ph]

    2021 arXiv

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    Model independent analysis of coupled-channel scattering: A deep learning approach,

    Denny Lane B. Sombillo, Yoichi Ikeda, Toru Sato, and Atsushi Hosaka, “Model independent analysis of coupled-channel scattering: A deep learning approach,” Phys. Rev. D104, 036001 (2021), arXiv:2105.04898 [hep-ph]

    2021 arXiv

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    Unveiling the pole structure of S- matrix using deep learning,

    Denny Lane B. Sombillo, Yoichi Ikeda, Toru Sato, and Atsushi Hosaka, “Unveiling the pole structure of S- matrix using deep learning,” Rev. Mex. Fis. Suppl.3, 0308067 (2022), arXiv:2104.14182 [hep-ph]

    2022 arXiv

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    Status of the Λ(1405),

    Maxim Mai, “Status of the Λ(1405),” Few Body Syst. 59, 61 (2018)

    2018

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    Towards the Minimal Spectrum of Excited Baryons,

    J. Landay, M. Mai, M. D¨ oring, H. Haberzettl, and K. Nakayama, “Towards the Minimal Spectrum of Excited Baryons,” Phys. Rev. D99, 016001 (2019), arXiv:1810.00075 [nucl-th]

    2019 arXiv

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    Model selection for pion photoproduction,

    R. Molina, Justin Landay, Bin Hu, Michael Doring, and Cesar Fern´ andez-Ram´ ırez, “Model selection for pion photoproduction,” PoSHadron2017, 135 (2018)

    2018

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    Ridge regression for minimizing the couplings of hyperon resonances in K+Λ photoproduction,

    Dimitrios Petrellis and Dalibor Skoupil, “Ridge regression for minimizing the couplings of hyperon resonances in K+Λ photoproduction,” Phys. Rev. C 107, 045206 (2023), arXiv:2212.14305 [nucl-th]

    2023 arXiv

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    Model selection for K+Σ−photoproduction within an isobar model,

    Petr Bydˇ zovsk´ y, Aleˇ s Ciepl´ y, Dimitrios Petrellis, Dalibor Skoupil, and Nicholas Zachariou, “Model selection for K+Σ−photoproduction within an isobar model,” Phys. Rev. C104, 065202 (2021), [Erratum: Phys.Rev.C 110, 029901 (2024)], arXiv:2106.15199 [nucl-th]

    2021 arXiv

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    Toward a generative modeling analysis of CLAS exclusive 2πphotoproduction,

    T. Alghamdiet al., “Toward a generative modeling analysis of CLAS exclusive 2πphotoproduction,” Phys. Rev. D108, 094030 (2023), arXiv:2307.04450 [hep-ph]

    2023 arXiv

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    Study for a model-independent pole determination of overlapping resonances,

    Daniele Binosi, Alessandro Pilloni, and Ralf- Arno Tripolt, “Study for a model-independent pole determination of overlapping resonances,” Phys. Lett. B839, 137809 (2023), arXiv:2205.02690 [hep-ph]

    2023 arXiv

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    New insights into the pole parameters of the Λ(1380), the Λ(1405) and the Σ(1385),

    Daniel Sadasivan, Maxim Mai, Michael D¨ oring, Ulf- G. Meißner, Felipe Amorim, John Paul Klucik, Jun- Xu Lu, and Li-Sheng Geng, “New insights into the pole parameters of the Λ(1380), the Λ(1405) and the Σ(1385),” Front. Phys.11, 1139236 (2023), arXiv:2212.10415 [nucl-th]

    2023 arXiv

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    New insights into the nature of the Λ(1380) and Λ(1405) resonances away from the SU(3) limit,

    Feng-Kun Guo, Yuki Kamiya, Maxim Mai, and Ulf-G. Meißner, “New insights into the nature of the Λ(1380) and Λ(1405) resonances away from the SU(3) limit,” Phys. Lett. B846, 138264 (2023), arXiv:2308.07658 [hep-ph]

    2023 arXiv

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    Testing chiral unitary models for the Λ(1405) in K+πΣ photoproduction,

    P. C. Bruns, A. Ciepl´ y, and M. Mai, “Testing chiral unitary models for the Λ(1405) in K+πΣ photoproduction,” Phys. Rev. D106, 074017 (2022)

    2022

  91. [99]

    Nucleon resonance parameters from Roy–Steiner equations,

    Martin Hoferichter, Jacobo Ruiz de Elvira, Bastian Kubis, and Ulf-G. Meißner, “Nucleon resonance parameters from Roy–Steiner equations,” Phys. Lett. B 853, 138698 (2024), arXiv:2312.15015 [hep-ph]

    2024 arXiv

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    Theoretical approaches to low energy ¯KNinteractions,

    Ales Ciepl´ y and Maxim Mai, “Theoretical approaches to low energy ¯KNinteractions,” EPJ Web Conf.130, 02001 (2016), arXiv:1610.06444 [nucl-th]

    2016 arXiv

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    On the pole content of coupled channels chiral approaches used for the ¯KNsystem,

    A. Ciepl´ y, M. Mai, Ulf-G. Meißner, and J. Smejkal, “On the pole content of coupled channels chiral approaches used for the ¯KNsystem,” Nucl. Phys. A954, 17–40 (2016), arXiv:1603.02531 [hep-ph]. 13

    2016 arXiv

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    Constraints on the chiral unitary ¯KNamplitude fromπΣK + photoproduction data,

    Maxim Mai and Ulf-G. Meißner, “Constraints on the chiral unitary ¯KNamplitude fromπΣK + photoproduction data,” Eur. Phys. J. A51, 30 (2015), arXiv:1411.7884 [hep-ph]

    2015 arXiv

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    S=−1 meson-baryon interaction and the role of isospin filtering processes,

    Albert Feijoo, Volodymyr Magas, and Angels Ramos, “S=−1 meson-baryon interaction and the role of isospin filtering processes,” Phys. Rev. C99, 035211 (2019), arXiv:1810.07600 [hep-ph]

    2019 arXiv

  96. [104]

    Coupled-channels analysis of pion andηelectroproduction within the J¨ ulich-Bonn- Washington model,

    Maxim Mai, Michael D¨ oring, Carlos Granados, Helmut Haberzettl, Jackson Hergenrather, Ulf-G. Meißner, Deborah R¨ onchen, Igor Strakovsky, and Ron Workman (J¨ ulich-Bonn-Washington), “Coupled-channels analysis of pion andηelectroproduction within the J¨ ulich-Bonn- Washington ...

    2022 arXiv

  97. [105]

    Inclusion ofKΛ electroproduction data in a coupled channel analysis,

    M. Mai, J. Hergenrather, M. D¨ oring, T. Mart, Ulf-G. Meißner, D. R¨ onchen, and R. Workman (J¨ ulich–Bonn–Washington), “Inclusion ofKΛ electroproduction data in a coupled channel analysis,” Eur. Phys. J. A59, 286 (2023), arXiv:2307.10051 [nucl-th]

    2023 arXiv

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    Statistical error analysis for phenomenological nucleon-nucleon potentials,

    R. Navarro Perez, J. E. Amaro, and E. Ruiz Arriola, “Statistical error analysis for phenomenological nucleon-nucleon potentials,” Phys. Rev. C89, 064006 (2014), arXiv:1404.0314 [nucl-th]

    2014 arXiv

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    Coarse-grained potential analysis of neutron-proton and proton-proton scattering below the pion production threshold,

    R. Navarro P´ erez, J. E. Amaro, and E. Ruiz Arriola, “Coarse-grained potential analysis of neutron-proton and proton-proton scattering below the pion production threshold,” Phys. Rev. C88, 064002 (2013), [Erratum: Phys.Rev.C 91, 029901 (2015)], arXiv:1310.2536 [nucl- th]

    2013 arXiv

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    Review of particle physics,

    S. Navaset al.(Particle Data Group), “Review of particle physics,” Phys. Rev. D110, 030001 (2024)

    2024

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    Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis,

    R. Garcia-Martin, R. Kaminski, J. R. Pelaez, and J. Ruiz de Elvira, “Precise determination of the f0(600) and f0(980) pole parameters from a dispersive data analysis,” Phys. Rev. Lett.107, 072001 (2011), arXiv:1107.1635 [hep-ph]

    2011 arXiv

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    Light scalars as tetraquarks or two- meson states from large N(c) and unitarized chiral perturbation theory,

    J. R. Pelaez, “Light scalars as tetraquarks or two- meson states from large N(c) and unitarized chiral perturbation theory,” Mod. Phys. Lett. A19, 2879– 2894 (2004), arXiv:hep-ph/0411107

    2004 arXiv

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    (O’Reilly Media, Sebastopol, CA, 2019)

    Joel Grus,Data Science from Scratch: First Principles with Python, 2nd ed. (O’Reilly Media, Sebastopol, CA, 2019). 14 Appendix A: Additional Numerical Tests: Network Architecture The architecture of the neural network is in general somewhat arbitrary. To provide some level of ...

    2019

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    We note that thereluactivation function, the Adam optimizer, and the mean squared error loss function are standard and have not been fine-tuned for a specific problem at hand

    The neural network is trained with the Adam optimizer. We note that thereluactivation function, the Adam optimizer, and the mean squared error loss function are standard and have not been fine-tuned for a specific problem at hand. The leakyrelufor the output layer was chosen b...

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.