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This paper claims that parametric matrix models (PMMs) can replace expensive in-medium similarity renormalization group (IMSRG) nuclear-matter calculations with a fast, accurate surrogate equipped with rigorously calibrated confidence inter

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2026-08-01 11:44 UTC pith:UAMGHSFD

load-bearing objection Strong emulator-validation paper with a real and self-admitted gap between the conformal-calibrated regime and the extrapolated saturation-point predictions. the 3 major comments →

arxiv 2607.19773 v1 pith:UAMGHSFD submitted 2026-07-22 nucl-th

PMM-IMSRG emulator for the nuclear equation of state with quantified uncertainties

Patrick Cook , Kang Yu , Christian Drischler , Scott K. Bogner This is my paper
classification nucl-th
keywords emulatorIMSRGnuclear equation of stateuncertainty quantificationconformal predictionparametric matrix modelschiral effective field theorythree-nucleon forces
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper introduces a hybrid emulator that replaces expensive in-medium similarity renormalization group (IMSRG) calculations of the nuclear equation of state (EOS) with a fast surrogate built from parametric matrix models (PMMs). The emulator learns low-dimensional representations of the Hamiltonian itself, preserving the physics of the underlying chiral interaction while predicting ground-state energies across low-energy constants, densities, basis sizes, and flow parameters. The supportive uncertainty estimate uses split conformal prediction, converting a sensitivity-based heuristic into finite-sample confidence intervals that track requested coverage to within a few percent on withheld data. The payoff is demonstrated by a Bayesian fit of three-nucleon couplings, including the quark-mass-dependent F2 term, to empirical saturation properties — a workflow that would be computationally prohibitive without the emulator.

Core claim

The paper's central claim is that an implicit-reduced-basis emulator — a PMM that learns the compressed Hamiltonian operators rather than the many-body wavefunctions — reproduces IMSRG nuclear-matter energies accurately across the parameter space while accelerating the calculation by about five orders of magnitude. This makes rigorous UQ of the nuclear EOS computationally routine. Using the trained emulator, the authors propagate both parametric and emulator uncertainties to pure neutron and symmetric matter, and carry out a Bayesian calibration of the N2LO three-nucleon couplings cD, cE, and F2 against empirical saturation properties. They find that adding the quark-mass-dependent F2 intera

What carries the argument

The key object is the parametric matrix model (PMM): the emulator learns a universal parameterized partial isometry u(Ns, Yp, n) = exp(i Σ fj mj)(:,1:k) that compresses the free-space Hamiltonian to a small 'in-medium' matrix whose exact diagonalization yields the ground-state energy (Sec. III, Eq. 24). The exponential finite-flow correction E = E0 + Σ αi exp(−βi s) (Eq. 20) handles the IMSRG s-dependence. The UQ machinery is split conformal prediction: a calibration set (disjoint from training/testing) converts three sensitivity/distance heuristics into half-interval widths with guaranteed coverage, and the authors estimate the error quantile function from 500 conformal levels for likelihoo

Load-bearing premise

The emulator's predictions at the physical limit — infinitely long flow and infinitely many single-particle states — must remain accurate even though the training data deliberately stops at 15 closed shells and modest s-values, so the learned universal forms carry the full burden of extrapolation.

What would settle it

Take a few LEC sets not in the training data, run the full IMSRG at the largest model space (25 closed shells) and at long flow times, and compare the resulting energies and saturation-derived quantities against the emulator's conformal intervals; if coverage falls below the requested rate or the saturation point moves by more than the quoted credible interval, the extrapolation assumption fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • IMSRG-based Bayesian parameter estimation for the nuclear EOS becomes computationally routine, instead of prohibitive, because each call costs microseconds rather than hours.
  • The conformal prediction UQ is a general recipe that can be attached to any smooth emulator, not just to PMMs or to EOS calculations.
  • The calibrated posteriors can be propagated to the EOS of pure neutron matter and symmetric matter, where the paper finds EFT truncation errors dominate in SNM and LEC priors dominate in PNM.
  • The trained emulator can extract expectation values of individual Hamiltonian pieces (cD, cE, F2, V0), providing a new diagnostic for why particular three-nucleon forces matter.
  • The framework is positioned for extension to proton-fraction and temperature dependence needed for astrophysical EOS tables.

Where Pith is reading between the lines

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

  • A stress test for the extrapolation would be retraining the emulator with a fraction of fully converged samples (large Ns, large s) in the training set; if the saturation-point posterior shifts significantly, the current inductive bias is doing more work than the data.
  • Nothing in the conformal-calibration scheme depends on the PMM architecture, so the same uncertainty pipeline could be applied to eigenvector continuation or other reduced-basis emulators, letting papers compare UQ quality directly.
  • The paper deliberately leaves EFT truncation errors out of the Bayesian likelihood; adding the truncation-error model it already uses for the EOS bands to the likelihood would be a natural next step and would likely widen the F2 posterior.
  • The reported F2 constraint of 0.16+0.32−0.79 fm4 is consistent with zero; a dedicated few-body fit including the triton vertex in the same framework would test whether this weak constraint is an artifact of the exploratory Hamiltonian or real.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper introduces a hybrid emulator for IMSRG calculations of nuclear matter, combining a parametric matrix model (PMM) for the Hamiltonian with learned exponential corrections in the IMSRG flow parameter s and the basis size N_s. The emulator's uncertainty estimates are obtained with split conformal prediction and are validated on withheld IMSRG test data that are deliberately more converged and larger in basis than the training data. The authors use the emulator to study saturation properties of symmetric nuclear matter, to constrain the N2LO 3N LECs c_D, c_E, and F_2 by a Bayesian fit to empirical saturation properties, and to propagate LEC, emulator, and EFT-truncation uncertainties to the PNM and SNM equations of state. They report approximately five orders of magnitude speedup over direct IMSRG evaluation.

Significance. If the method's central claims hold, this is a significant contribution: it demonstrates a practical path to emulating nonperturbative IMSRG calculations across LECs, density, flow parameter, and basis size, turning previously prohibitive Bayesian parameter estimation into a routine computation. The paper has several concrete strengths: the training/validation/calibration/test partitioning is explicit and stratified; the emulator is tested on genuinely withheld, harder test data; the conformal calibration tracks requested coverage closely (maximum under-coverage 0.55% for confidence levels above 10%); and the open-source pyPMM library makes the implementation reproducible. The Bayesian application is labeled exploratory, and the paper is candid about several limitations, including the omission of EFT truncation errors from the calibration and the breakdown of coverage guarantees for derived quantities.

major comments (3)
  1. [Sec. III.A, Eqs. (20), (24), (33)-(34), Fig. 3] The split-conformal validation is performed only for finite s and N_s. Figure 3 shows that training and validation data contain at most 15 and 20 closed shells, respectively, and mostly unconverged s; calibration and test data reach 25 shells and near-converged s, but no point has s=∞ or N_s=∞. Nevertheless, the saturation predictions in Figs. 6, 9, and 10 are evaluated at {N_s,s}={∞,∞}. The exponential finite-s ansatz (20) and the universal partial-isometry ansatz (24) are therefore load-bearing for the saturation-point and derived L/K/S results, not the conformal machinery. The uncertainty heuristic also explicitly excludes s and N_s from the distance-to-training-set term (Sec. III.A.1), so it cannot flag this extrapolation. I request a direct validation of emulated saturation properties against IMSRG saturation calculations at the largest shells and near-converged s, or an explicit se
  2. [Sec. IV.C.1, Eqs. (45)-(56)] The likelihood (56) uses quantile functions q_X for X∈{n_sat,E_sat,S,L,K} that are constructed from conformal intervals. However, Sec. III.A.2 states that propagating emulator uncertainties to derived quantities such as the incompressibility "breaks the coverage guarantees"; the same applies to the derivative-based L and S and to the density minimum defining n_sat. Thus the posterior distributions in Figs. 9-10 and the propagated bands in Figs. 11-12 treat as exact the very intervals whose coverage is not guaranteed in the extrapolated regime. If the s,N_s extrapolation is biased, the F_2 constraint and the EOS bands inherit the bias. Please either calibrate the derived-quantity intervals on a dedicated validation set or add an explicit extrapolation-bias term to the discrepancy model.
  3. [Sec. IV.B, Eq. (40)] The c_E(c_D) uncertainty used to generate Figs. 7 and 8 is a Gaussian process with an RBF kernel whose hyperparameters σ_f=0.12 and ℓ=10 are described as "somewhat arbitrary"; the GP is not conditioned on the actual triton-binding data or on an EFT truncation model. The resulting "LEC uncertainty" and "total uncertainty" bands are therefore not quantitative in the same sense as the emulator's conformal intervals. Given that these figures are presented as uncertainty bands, either calibrate this GP from the underlying few-body calculations or explicitly label the bands as exploratory sensitivity ranges.
minor comments (4)
  1. [Sec. IV.A, Fig. 6] The text says 20,000 random 3N LEC samples are used, while the figure caption says 10,000. Please make the numbers consistent.
  2. [Fig. 9] The caption contains a typo: "the uniform prior enforces the constraint |cD ≤ 5|" should read |c_D|≤5.
  3. [Sec. IV.C, footnote 10] The calibration omits EFT truncation errors, and the text is transparent about this. However, because the abstract and summary claim "quantified uncertainties" and "trustworthy confidence intervals" without this qualification, I recommend adding an explicit qualifier to the abstract and to the discussion of the F_2 constraint that the calibration accounts only for emulator error.
  4. [Sec. IV.D] The BUQEYE truncation-error model is applied pointwise in density, and the text notes that it neglects density correlations; this is appropriate as a stated limitation but should also be mentioned wherever the total uncertainty bands in Figs. 11-12 are summarized.

Circularity Check

0 steps flagged

No significant circularity: emulator is validated on withheld IMSRG data, LEC calibration is an explicit fit, and the s/N_s extrapolation is a stated correctness limitation, not a circular step.

full rationale

The central claim is that a PMM-based surrogate accurately emulates IMSRG nuclear-matter energies with calibrated uncertainties. That claim is tested against withheld IMSRG calculations (Figs. 4 and 5), so the accuracy and coverage statements do not reduce to the training data or to fitted parameters renamed as predictions. The LEC constraints in Sec. IVC are explicitly fits to empirical saturation properties, not predictions: the paper states it is 'calibrating 3N forces to empirical saturation properties' and repeatedly labels the interactions 'exploratory', and Eqs. (50)-(57) define a likelihood based on those empirical values. Propagating the resulting LEC posterior to the EOS is legitimate model-based uncertainty propagation. The self-citations to Refs. [23,24,32] supply the IMSRG nuclear-matter framework and the PMM formalism, but the present paper describes the equations, trains the emulator on IMSRG data, and evaluates it on disjoint withheld data; the load is not carried by citation alone. The stated limitations—that propagating emulator uncertainties to derived saturation quantities 'breaks the coverage guarantees' (Sec. IIIA2) and that EFT truncation errors are omitted from the calibration (Sec. IVC)—are correctness and scope limitations about extrapolation beyond the conformal calibration support, not instances of a prediction being equivalent to its inputs by construction. No equation in the paper is shown to reduce to another by definition, and no fitted parameter is presented as an independent prediction. Therefore, no significant circularity is present.

Axiom & Free-Parameter Ledger

5 free parameters · 7 axioms · 0 invented entities

Most physical input is inherited from chiral EFT and IMSRG literature. The new inferential machinery contributes a large set of learned emulator parameters and the assumed exponential/universal functional forms; the physical LECs fitted here are free parameters in the calibration, and several hyperparameters are chosen by hand.

free parameters (5)
  • PMM trainable parameters (<30,000) = not enumerated
    Optimized to minimize the wMSE/wVAR loss on the IMSRG training set; encode implicit reduced basis and flow corrections.
  • cD, cE = cD = -2.8^{+3.2}_{-1.6}, cE = -1.21^{+0.29}_{-0.24} (posterior medians)
    Bayesian fit to empirical saturation properties, with a GP band around the triton-binding cD(cE) curve from Ref. [46].
  • F2 = 0.16^{+0.32}_{-0.79} fm^4
    Fitted in the same Bayesian calibration to empirical saturation properties; posterior is consistent with zero at 68%.
  • GP kernel hyperparameters sigma_f, l = sigma_f = 0.12, l = 10
    Chosen by hand for the cE(cD) uncertainty band; the paper calls this band "somewhat arbitrary symmetric uncertainty."
  • BUQEYE truncation hyperparameters mu0, tau0, y_ref = 1, 1, 16 MeV
    Chosen for the EFT truncation error model in Sec. IV.D.
axioms (7)
  • domain assumption IMSRG(2) with NO2B truncation closes the flow equations and accurately represents nuclear-matter energies.
    Section II.C; the high-fidelity IMSRG results used as training/test truth rely on this truncation.
  • domain assumption Exponential finite-s ansatz: E_IMSRG(s) = E0 + sum_i alpha_i(X) exp(-beta_i(X) s).
    Eq. (20), Section III; used to emulate finite-s dependence and extrapolate to s→∞.
  • ad hoc to paper The universal partial-isometry form Eq. (24) can approximate the true U(Ns,Yp,n) for sufficiently large l and expressive f_j.
    Section III; no proof is supplied, only the assertion that it can represent any parameterized partial isometry.
  • domain assumption Split-conformal coverage guarantees apply to the stratified calibration/test split.
    Section III.A; exchangeability is required, but the test set deliberately favors more-converged and larger-Ns samples.
  • domain assumption The EMN 450 MeV chiral potentials with affine 3N LEC dependence represent the nuclear interaction.
    Section III; only cD, cE, D2, F2 are varied and all other LECs are fixed.
  • domain assumption PNM is independent of cD and cE for the nonlocal regulators used.
    Section III, citing Ref. [48].
  • domain assumption The empirical saturation point t9 distribution and the priors for S, L, K in Eqs. (41)–(42) encode the physical constraints used for calibration.
    Section IV.C; the posterior LECs inherit these assumptions.

pith-pipeline@v1.3.0-alltime-deepseek · 24372 in / 13241 out tokens · 125508 ms · 2026-08-01T11:44:36.465796+00:00 · methodology

0 comments
read the original abstract

We introduce a hybrid emulator for in-medium similarity renormalization group (IMSRG) calculations of nuclear matter, based on chiral nucleon-nucleon and three-nucleon interactions and an implicit-reduced-basis method emulator constructed from parametric matrix models (PMMs) which is capable of rigorously estimating its uncertainties via conformal predictions. The resulting PMM-IMSRG emulator enables fast and accurate predictions with trustworthy confidence intervals of the nuclear equation of state (EOS) across a wide range of input parameters, including low-energy couplings, IMSRG flow parameters, densities, and basis sizes. This framework provides the foundation for principled uncertainty quantification of the nuclear EOS and enables computationally demanding applications such as Bayesian parameter estimation using our IMSRG calculations. As a first application, we present results for the coupling constants of the two quark-mass-dependent three-nucleon interactions, recently identified to contribute at next-to-next-to-leading order in the chiral expansion based on a renormalization-group analysis, by fitting them to empirical saturation properties. We then propagate both parametric and emulator uncertainties to the EOS in the limits of pure neutron matter and symmetric nuclear matter.

Figures

Figures reproduced from arXiv: 2607.19773 by Christian Drischler, Kang Yu, Patrick Cook, Scott K. Bogner.

Figure 1
Figure 1. Figure 1: FIG. 1. A schematic view of IMSRG decoupling [ [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comprehensive diagram of the PMM–IMSRG em [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The stratified partitioning of the IMSRG samples [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Comparison of PMM-predicted energies at the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Saturation point distributions in SNM obtained from [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Confidence regions of the EOS in the limit of SNM at [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Low-density EOS parameters associated with the [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Corner plot showing the posterior distributions and [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Same as Fig [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Median expectation values of each term in the emu [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗

discussion (0)

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Reference graph

Works this paper leans on

92 extracted references · 45 linked inside Pith

  1. [1]

    Conformal predictions We quantify our emulator uncertainties using split conformal predictions,7 which provide distribution-free finite-sample confidence guarantees that rely only on the exchangeability of data.8 For a comprehensive introduc- tiontothistechnique, wereferthereadertoRefs.[54,55]. The core concepts are an uncertainty heuristic and a calibrat...

  2. [2]

    Devise a functionU (X) which encodes a heuristic for the uncertainty of the emulator

  3. [3]

    Calculate the value of the score function—defined as the residual over the uncertainty heuristic—for each point in the calibration set S(Xi) = E(Xi) − ˆEi U (Xi) . (35)

  4. [4]

    8See Refs

    For a desired miscoverage levelα (or coverage prob- ability 1 − α), define ˆq to be the ⌈(1 − α)(n + 1)⌉ n (36) 7The proposed conformal-prediction-based estimation of emu- lator uncertainty is broadly applicable and not limited to IMSRG calculations of the nuclear EOS. 8See Refs. [53] for recent applications of conformal predictions to quantifying uncerta...

  5. [5]

    ˆq is the multiplicative correction to the uncertainty heuristic, and thus the conformalized model which returns the lower and upper bounds of the confi- dence interval with miscoverage levelα for a test point X denoted by Cα(X) is Cα(X) = E(X) − ˆq U (X), E(X) + ˆq U (X) . (37) Although the conformalized model has statically guar- anteed coverage [56], t...

  6. [6]

    The sensitivity of the trained emulator to pertur- bations in the trainable parameters, SΘ(X) = 1 ℓ(Θ) ∂E ∂Θ X ⊙ Θ 2 2 , (38) where ⊙ is the elementwise product,Θ denotes the vector of all trainable parameters of the model, and ℓ(Θ) denotes the number of trainable parameters

  7. [7]

    The sensitivity of the trained emulator to pertur- bations in the input values, SX (X) = 1 ℓ(Xcont) ∂E ∂Xcont X ⊙ δ(Xcont) 2 2 , (39) where Xcont denotes only the continuous input fea- tures, ℓ(Xcont) denotes the number of continuous input features, andδ(Xcont) denotes the character- istic scale of each of the continuous input features, which we take to b...

  8. [8]

    The uncertainty heuristic for a test point is the normal- ized sum of these three contributions

    The distance of the test point to the training set, Sd(X), defined by the mean unweighted Gower’s distance between the test point and all points in the training set within a distance threshold equal to the median unweighted Gower’s distance between all pairs of points in the training set, excluding any features that can have infinite values (s and Ns) [57...

  9. [9]

    Accuracy of the emulator uncertainty estimate We first demonstrate the accuracy of our emulator on withheld test data across both SNM and PNM at N2LO and N3LO in Fig. 4. The test data includes both SNM and PNM, varies all LECs considered in this work (cD, cE, D2, F2) and the nuclear density, and includes data of themostconvergedIMSRGresultsforthelargestnu...

  10. [10]

    While neglecting these correlations may lead to misestima- tion of EFT predictions, rigorously quantifying and incorporating these uncertainties remains a work in progress [63]

    Bayesian fit protocol The empirical observables used to constrain these LECs include the saturation density (nsat), saturation 10LEC uncertainties and the EFT truncation errors are corre- lated. While neglecting these correlations may lead to misestima- tion of EFT predictions, rigorously quantifying and incorporating these uncertainties remains a work in...

  11. [11]

    We use 32 random walkers, initialized at the maximum a posteriori (MAP) estimate plus random perturbations, discard 4000 burn-in steps, and generate 20 000 production steps

    LEC constraints and predictions for the low-density EOS With the standard Monte Carlo sampler implemented in the Python packageemcee [68], we sample the poste- rior distribution of the LECs. We use 32 random walkers, initialized at the maximum a posteriori (MAP) estimate plus random perturbations, discard 4000 burn-in steps, and generate 20 000 production...

  12. [12]

    Drischler, J

    C. Drischler, J. W. Holt, and C. Wellenhofer, Annu. Rev. Nucl. Part. Sci.71, 403 (2021), arXiv:2101.01709

    Pith/arXiv arXiv 2021

  13. [13]

    Sorensenet al., Prog

    A. Sorensenet al., Prog. Part. Nucl. Phys.134, 104080 (2024), arXiv:2301.13253

    Pith/arXiv arXiv 2024

  14. [14]

    Kumaret al.(MUSES), Living Rev

    R. Kumaret al.(MUSES), Living Rev. Rel.27, 3 (2024), arXiv:2303.17021 [nucl-th]

    Pith/arXiv arXiv 2024

  15. [15]

    Chatziioannou, H

    K. Chatziioannou, H. T. Cromartie, S. Gandolfi, I. Tews, D. Radice, A. W. Steiner, and A. L. Watts, Rev. Mod. Phys. 97, 045007 (2025), arXiv:2407.11153

    arXiv 2025

  16. [16]

    Agarwal, J

    K. Agarwal, J. Jahan, B. Kardan, P. T. H. Pang, T. Re- ichert, and A. C. Semposki, (2025), arXiv:2511.20378

    Pith/arXiv arXiv 2025

  17. [17]

    Drischler, K

    C. Drischler, K. S. McElvain, and P. Arthuis, (2026), arXiv:2603.24532

    arXiv 2026

  18. [18]

    Keller, C

    J. Keller, C. Wellenhofer, K. Hebeler, and A. Schwenk, Phys. Rev. C103, 055806 (2021), arXiv:2011.05855

    Pith/arXiv arXiv 2021

  19. [19]

    Keller, K

    J. Keller, K. Hebeler, and A. Schwenk, Phys. Rev. Lett. 130, 072701 (2023), arXiv:2204.14016 [nucl-th]

    Pith/arXiv arXiv 2023

  20. [20]

    J. W. Holt and N. Kaiser, Phys. Rev. C 95, 034326 (2017), arXiv:1612.04309

    Pith/arXiv arXiv 2017

  21. [21]

    P. Wen, J. W. Holt, and A. Blackburn, (2024), arXiv:2412.19777 [nucl-th]

    Pith/arXiv arXiv 2024

  22. [22]

    Brolli, C

    S. Brolli, C. Barbieri, and E. Vigezzi, Phys. Rev. Lett. 134, 182502 (2025), arXiv:2501.02646 [nucl-th]

    Pith/arXiv arXiv 2025

  23. [23]

    Hagen, T

    G. Hagen, T. Papenbrock, A. Ekström, K. A. Wendt, G. Baardsen, S. Gandolfi, M. Hjorth-Jensen, and C. J. Horowitz, Phys. Rev. C 89, 014319 (2014), arXiv:1311.2925

    Pith/arXiv arXiv 2014

  24. [24]

    Baardsen, A

    G. Baardsen, A. Ekström, G. Hagen, and M. Hjorth-Jensen, Phys. Rev. C 88, 054312 (2013), arXiv:1306.5681

    Pith/arXiv arXiv 2013

  25. [25]

    W. G. Jiang, C. Forssén, T. Djärv, and G. Hagen, (2022), arXiv:2212.13203

    Pith/arXiv arXiv 2022

  26. [26]

    Lonardoni, I

    D. Lonardoni, I. Tews, S. Gandolfi, and J. Carlson, Phys. Rev. Res2, 022033(R) (2020), arXiv:1912.09411

    Pith/arXiv arXiv 2020

  27. [27]

    Arthuis, C

    P. Arthuis, C. Barbieri, F. Pederiva, and A. Roggero, Phys. Rev. C107, 044303 (2023), arXiv:2203.16167

    Pith/arXiv arXiv 2023

  28. [28]

    B. Fore, J. Kim, M. Hjorth-Jensen, and A. Lovato, Com- mun. Phys.8, 108 (2025), arXiv:2407.21207 [nucl-th]

    Pith/arXiv arXiv 2025

  29. [29]

    Lovato, G

    A. Lovato, G. Carleo, B. Fore, M. Hjorth-Jensen, J. Kim, A. Rios, and N. Rocco, (2026), arXiv:2602.13826 [nucl- th]

    arXiv 2026

  30. [30]

    R. Hu, S. Jin, X. Zhen, H. Shang, J. Pei, F. Xu, and F. Marino, (2025), 10.1103/q4p2-r1bt, arXiv:2508.09252 [nucl-th]

    Pith/arXiv arXiv 2025

  31. [31]

    Marino, C

    F. Marino, C. Barbieri, and G. Colò, (2026), arXiv:2601.03763 [nucl-th]

    arXiv 2026

  32. [32]

    W. H. Dickhoff and C. Barbieri, Prog. Part. Nucl. Phys. 52, 377 (2004), arXiv:nucl-th/0402034

    Pith/arXiv arXiv 2004

  33. [33]

    Rios, Front

    A. Rios, Front. in Phys.8, 387 (2020), arXiv:2006.10610 [nucl-th]

    Pith/arXiv arXiv 2020

  34. [34]

    O. C. Udiani, Extending the In-Medium Similarity Renormalization Group to Nuclear Matter with Novel In- sights on Unitary Coupled-Cluster Theory, Ph.D. thesis, Michigan State University, East Lansing, MI (2025)

    2025

  35. [35]

    In-medium similarity renormalization group calculations of nuclear matter,

    O. Udiani, K. Yu, C. Drischler, S. J. Novario, and S. K. Bogner, “In-medium similarity renormalization group calculations of nuclear matter,” (2026), in prep

    2026

  36. [36]

    X. Zhen, R. Hu, H. Shang, J. Chen, J. Pei, and F. Xu, Phys. Lett. B862, 139350 (2025), arXiv:2501.02479

    Pith/arXiv arXiv 2025

  37. [37]

    Duguet, A

    T. Duguet, A. Ekström, R. J. Furnstahl, S. König, and D. Lee, Rev. Mod. Phys. 96, 031002 (2024), arXiv:2310.19419 [nucl-th]

    Pith/arXiv arXiv 2024

  38. [38]

    Drischler, J

    C. Drischler, J. A. Melendez, R. J. Furnstahl, A. J. Garcia, and X. Zhang, Front. Phys. 10, 92931 (2023), supplemental, interactive Python code can be found on the companion websitehttps://github.com/buqeye/ frontiers-emulator-review, arXiv:2212.04912

    Pith/arXiv arXiv 2023

  39. [39]

    C. L. Armstrong, B. T. Reed, T. Plohr, H. Rose, S. De, R. Somasundaram, and I. Tews, (2026), arXiv:2601.05999

    arXiv 2026

  40. [40]

    C. L. Armstrong, P. Giuliani, K. Godbey, R. Somasun- daram, andI.Tews,Phys.Rev.Lett. 135,142501(2025), arXiv:2502.03680 [nucl-th]

    arXiv 2025

  41. [41]

    Gandolfi, and I

    R.Somasundaram, C.L.Armstrong, P.Giuliani, K.God- bey, S. Gandolfi, and I. Tews, Phys. Lett. B866, 139558 (2025), arXiv:2404.11566 [nucl-th]

    Pith/arXiv arXiv 2025

  42. [42]

    W. G. Jiang, C. Forssén, T. Djärv, and G. Hagen, Phys. Rev. C109, 064314 (2024), arXiv:2212.13216

    Pith/arXiv arXiv 2024

  43. [43]

    P. Cook, D. Jammooa, M. Hjorth-Jensen, D. D. Lee, and D. Lee, Nature Communications16, 5929 (2025)

    2025

  44. [44]

    Frame, R

    D. Frame, R. He, I. Ipsen, D. Lee, D. Lee, and E. Rrapaj, Phys. Rev. Lett.121, 032501 (2018), arXiv:1711.07090. 17

    Pith/arXiv arXiv 2018

  45. [45]

    J. A. Melendez, C. Drischler, R. J. Furnstahl, A. J. Garcia, and X. Zhang, J. Phys. G 49, 102001 (2022), arXiv:2203.05528 [nucl-th]

    Pith/arXiv arXiv 2022

  46. [46]

    Vernik, K

    U. Vernik, K. Hebeler, and A. Schwenk, (2025), arXiv:2512.20454

    Pith/arXiv arXiv 2025

  47. [47]

    Cirigliano, M

    V. Cirigliano, M. Dawid, W. Dekens, and S. Reddy, Phys. Rev. Lett.135, 022501 (2025)

    2025

  48. [48]

    Hergert, S

    H. Hergert, S. K. Bogner, T. D. Morris, A. Schwenk, and K. Tsukiyama,Memorial Volume in Honor of Gerald E. Brown, Physics Reports621, 165 (2016)

    2016

  49. [49]

    In-medium similarity renormalization group approach to the nuclear many-body problem,

    H. Hergert, S. K. Bogner, J. G. Lietz, T. D. Morris, S. J. Novario, N. M. Parzuchowski, and F. Yuan, “In-medium similarity renormalization group approach to the nuclear many-body problem,” in An Advanced Course in Com- putational Nuclear Physics: Bridging the Scales from Quarks to Neutron Stars, edited by M. Hjorth-Jensen, M. P. Lombardo, and U. van Kolck...

    2017

  50. [50]

    Hergert, Phys

    H. Hergert, Phys. Scripta 92, 023002 (2017), arXiv:1607.06882

    Pith/arXiv arXiv 2017

  51. [51]

    S. R. Stroberg, S. K. Bogner, H. Hergert, and J. D. Holt, Annu. Rev. Nucl. Part. Sci. 69, 307 (2019), arXiv:1902.06154

    Pith/arXiv arXiv 2019

  52. [52]

    Marino, W

    F. Marino, W. Jiang, and S. J. Novario, Phys. Rev. C 110, 054322 (2024), arXiv:2407.17098 [nucl-th]

    arXiv 2024

  53. [53]

    Binder, J

    S. Binder, J. Langhammer, A. Calci, P. Navratil, and R. Roth, Phys. Rev. C 87, 021303 (2013), arXiv:1211.4748 [nucl-th]

    Pith/arXiv arXiv 2013

  54. [54]

    R. Roth, S. Binder, K. Vobig, A. Calci, J. Langhammer, and P. Navratil, (2011), arXiv:1112.0287

    Pith/arXiv arXiv 2011

  55. [55]

    Djärv, A

    T. Djärv, A. Ekström, C. Forssén, and G. R. Jansen, Phys. Rev. C 104, 024324 (2021), arXiv:2104.14820 [nucl-th]

    Pith/arXiv arXiv 2021

  56. [56]

    T. D. Morris, N. M. Parzuchowski, and S. K. Bogner, Phys. Rev. C92, 034331 (2015)

    2015

  57. [57]

    Drischler, K

    C. Drischler, K. Hebeler, and A. Schwenk, Phys. Rev. Lett. 122, 042501 (2019), arXiv:1710.08220

    Pith/arXiv arXiv 2019

  58. [58]

    D. R. Entem, R. Machleidt, and Y. Nosyk, Phys. Rev. C 96, 024004 (2017), arXiv:1703.05454

    Pith/arXiv arXiv 2017

  59. [59]

    Hebeler and A

    K. Hebeler and A. Schwenk, Phys. Rev. C82, 014314 (2010), arXiv:0911.0483

    Pith/arXiv arXiv 2010

  60. [60]

    pyPMM: The Python Package for Parametric Matrix Models,

    P. Cook, “pyPMM: The Python Package for Parametric Matrix Models,” (2026)

    2026

  61. [61]

    Adam: Amethodforstochastic optimization,

    D.P.KingmaandJ.Ba,“Adam: Amethodforstochastic optimization,” (2017), arXiv:1412.6980 [cs.LG]

    Pith/arXiv arXiv 2017

  62. [62]

    Computational nuclear physics and post Hartree-Fock methods,

    J. G. Lietz, S. Novario, G. R. Jansen, G. Hagen, and M. Hjorth-Jensen, “Computational nuclear physics and post Hartree-Fock methods,” in An Advanced Course in Computational Nuclear Physics: Bridging the Scales from Quarks to Neutron Stars, edited by M. Hjorth- Jensen, M. P. Lombardo, and U. van Kolck (Springer International Publishing, Cham, 2017) pp. 293–399

    2017

  63. [63]

    Hergert, S

    H. Hergert, S. K. Bogner, J. G. Lietz, T. D. Morris, S. J. Novario, N. M. Parzuchowski, and F. Yuan, in An Advanced Course in Computational Nuclear Physics: Bridging the Scales from Quarks to Neutron Stars, edited by M. Hjorth-Jensen, M. P. Lombardo, and U. van Kolck (Springer International Publishing, Cham, 2017) pp. 477–570

    2017

  64. [64]

    H. Y. Dezdarani, R. Curry, and A. Gezerlis, Phys. Rev. C 113, 014004 (2026), arXiv:2507.08085

    arXiv 2026

  65. [65]

    A. N. Angelopoulos and S. Bates, Foundations and Trends in Machine Learning16, 494 (2023)

    2023

  66. [66]

    Distribution-free finite-sample guar- antees and split conformal prediction,

    R. Hulsman, “Distribution-free finite-sample guar- antees and split conformal prediction,” (2022), arXiv:2210.14735 [stat.ML]

    Pith/arXiv arXiv 2022

  67. [67]

    V. Vovk, A. Gammerman, and C. Saunders, inProceed- ings of the Sixteenth International Conference on Ma- chine Learning, ICML ’99 (Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 1999) p. 444–453

    1999

  68. [68]

    J. C. Gower, Biometrics27, 857 (1971)

    1971

  69. [69]

    Drischler, P

    C. Drischler, P. G. Giuliani, S. Bezoui, J. Piekarewicz, and F. Viens, Phys. Rev. C 110, 044320 (2024), arXiv:2405.02748

    Pith/arXiv arXiv 2024

  70. [70]

    Coester, S

    F. Coester, S. Cohen, B. Day, and C. M. Vincent, Phys. Rev. C1, 769 (1970)

    1970

  71. [71]

    C. E. Rasmussen and C. K. I. Williams,Gaussian Pro- cesses for Machine Learning, Adaptive computation and machine learning series (University Press Group Limited, Cambridge, MA, 2006)

    2006

  72. [72]

    J. A. Melendez, S. Wesolowski, and R. J. Furnstahl, Phys. Rev. C96, 024003 (2017), arXiv:1704.03308

    Pith/arXiv arXiv 2017

  73. [73]

    J. A. Melendez, R. J. Furnstahl, D. R. Phillips, M. T. Pratola, and S. Wesolowski, Phys. Rev. C100, 044001 (2019), arXiv:1904.10581

    Pith/arXiv arXiv 2019

  74. [74]

    N. L. Carter, R. J. Furnstahl, J. A. Melendez, and D. R. Phillips, (2026), arXiv:2602.05086

    arXiv 2026

  75. [75]

    B. T. Reed, F. J. Fattoyev, C. J. Horowitz, and J. Piekarewicz, Phys. Rev. Lett. 126, 172503 (2021), arXiv:2101.03193

    Pith/arXiv arXiv 2021

  76. [76]

    Roca-Maza and N

    X. Roca-Maza and N. Paar, Prog. Part. Nucl. Phys.101, 96 (2018), arXiv:1804.06256

    Pith/arXiv arXiv 2018

  77. [77]

    A. Giri, J. Kim, C. Drischler, C. Elster, and R. J. Furn- stahl, Phys. Rev. C113, 044001 (2026)

    2026

  78. [78]

    Casella and R

    G. Casella and R. L. Berger,Statistical Inference, 2nd ed., Chapman & Hall/CRC Texts in Statistical Science (Duxbury Press, Pacific Grove, CA, 2002)

    2002

  79. [79]

    D.Foreman-Mackey, D.W.Hogg, D.Lang, andJ.Good- man, PASP 125, 306 (2013), arXiv:1202.3665 [astro- ph.IM]

    Pith/arXiv arXiv 2013

  80. [80]

    Gnech, X

    A. Gnech, X. Zhang, C. Drischler, R. J. Furnstahl, A. Grassi, A. Kievsky, L. E. Marcucci, and M. Viviani, (2025), arXiv:2511.01844 [nucl-th]

    arXiv 2025

Showing first 80 references.