Pith. sign in

REVIEW 3 major objections 5 minor 60 references

Exploring the astrophysical origins of binary black holes using normalising flows

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The paper shows that normalising flows trained on population-synthesis output can interpolate binary black hole observables continuously across natal spin and common-envelope efficiency, enabling hierarchical inference from gravitational-wa

desk verdict A useful methods note showing normalizing flows can emulate population synthesis and beat KDEs, but the interpolation claim rests on one channel and one held-out point, and the headline astrophysical results live in the companion paper. read the letter →

arxiv 2508.19336 v1 pith:WCUOIIH3 submitted 2025-08-26 astro-ph.HE gr-qc

Storm Colloms , Christopher P L Berry , John Veitch , Michael Zevin This is my paper
classification astro-ph.HEgr-qc
keywords normalisingflowsbinaryblackholespopulationsynthesisgravitationalwaveshierarchicalinferencecommon-envelopeefficiencynatalspinsformationchannels
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

Binary black holes assemble through several formation channels, and matching gravitational-wave observations to detailed population-synthesis simulations is computationally expensive. This paper shows that normalising flows—neural-network emulators—can reproduce the distributions of binary black hole properties predicted by five formation channels and interpolate them across the natal spin χb and common-envelope efficiency αCE, where simulations were only run on a sparse grid. The interpolation turns a finite set of simulations into a continuous model, and the authors use it to infer posteriors over χb, αCE, and the branching fractions of the channels from the GWTC-3.0 catalogue. They find low natal spins, high common-envelope efficiency (αCE > 3.7), and a common-envelope channel that dominates the intrinsic population.

What carries the argument

Normalising flows: neural networks that learn an invertible, differentiable mapping from a simple base distribution to the target distribution of binary black hole observables (chirp mass, mass ratio, effective inspiral spin, redshift), conditioned on the population parameters (natal spin χb and common-envelope efficiency αCE). The flows are trained on output from five population-synthesis channels—common envelope, stable mass transfer, chemically homogeneous evolution, globular clusters, and nuclear star clusters—and provide a queryable, differentiable surrogate for the simulation output at any parameter point within the training range. This replaces kernel density estimates as the emulator

What would settle it

Run the leave-one-out interpolation test on each of the other four channels (stable mass transfer, chemically homogeneous, globular cluster, nuclear star cluster) at several held-out (χb, αCE) points; if any flow fails to beat a KDE baseline at a held-out point (positive KL difference), the claim that the flows interpolate accurately across all channels and the entire parameter range is false.

Watch

Extended reading notes

Core claim

The central claim is that normalising flows accurately emulate and interpolate population-synthesis distributions for binary black hole formation. Compared with the previous kernel density estimate emulators, the normalising flows reduce the average Kullback–Leibler divergence to the simulation data by 0.37–0.97 nat across the five channels, and a leave-one-out test on the common-envelope channel shows the flow reproduces a held-out simulation point as accurately as the flow trained on all data (KL difference −0.04 nat) and better than a KDE (−0.41 nat). The trained flows are then used for continuous hierarchical inference over χb, αCE, and the five channel branching fractions using GWTC-3.0

Load-bearing premise

The leave-one-out validation of interpolation is performed only for the common-envelope channel at one held-out parameter point; the analysis assumes the trained flows are equally accurate for all five channels and over the entire χb–αCE range, including regions and channels never so tested.

Editorial extensions

If this is right

  • Population parameters can now be inferred continuously over the χb–αCE plane without launching new population-synthesis runs at each proposal point, removing the main computational bottleneck in the analysis.
  • The inferred αCE > 3.7 supports the theoretical picture in which energy sources beyond the binary's orbital energy contribute to ejecting the common envelope.
  • The contrast between the intrinsic branching fractions (common-envelope ~0.91) and the more even detected fractions makes explicit how strongly selection biases shape the observed gravitational-wave catalogue.
  • The emulator's interpolated populations point to the most astrophysically interesting χb–αCE regions, where future detailed simulations would be most informative.

Reading between the lines

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

  • A natural extension is to condition the flows on additional population parameters, such as metallicity or supernova kick magnitude, provided the same leave-one-out validation is applied per channel; the paper does not show such cross-channel validation.
  • The branching-fraction measurement could be cross-checked against independent rate estimates from the same GWTC-3.0 data to test for emulator-induced bias, a check the paper does not perform.
  • If the interpolation accuracy holds outside the training grid, future catalogues could be re-analysed with shifted or expanded parameter ranges without rerunning the underlying population-synthesis codes.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper presents an emulator-based method for continuous population inference of binary black hole formation channels. Normalising flows are trained on population-synthesis outputs for five channels—common envelope, stable mass transfer, chemically homogeneous evolution, globular clusters, and nuclear star clusters—to approximate p(θ|λ) for chirp mass, mass ratio, effective inspiral spin, and redshift as a function of natal spin χ_b and common-envelope efficiency α_CE. The authors report that the flows outperform KDEs by 0.37–0.97 nat in average KL divergence, and they verify interpolation for the common-envelope channel by leaving out one training λ point, with a −0.04 nat KL difference relative to the full-flow emulator. They then apply the emulator to hierarchical inference with GWTC-3, finding low natal spin (χ_b=0.04^{+0.04}_{−0.01}), high common-envelope efficiency (α_CE>3.7 at 90% credibility), and a dominant underlying common-envelope branching fraction. The paper argues that this demonstrates that the flows are robust interpolators suitable for continuous multi-channel inference.

Significance. If the interpolation claim held for all five channels, this would be a useful methodological contribution: it would replace expensive population-synthesis runs with a fast differentiable emulator, permit interpolation over continuous astrophysical parameter ranges, and make multi-channel hierarchical inference tractable with current GW catalogs. The strengths are the direct quantitative comparison to KDEs, the leave-one-out test (albeit limited), and a concrete application to GWTC-3. The main issue is that the validation is currently too narrow to support the central claim, and the inference results are largely imported from the companion paper. The method is plausible and the paper is well written, but the evidence base needs strengthening.

major comments (3)
  1. [Section 2 (interpolation test)] The only interpolation validation is a leave-one-out test for the common-envelope channel at one λ point. This channel is special because α_CE affects only it, so the two-dimensional interpolation is exercised nowhere else. Stable mass transfer, chemically homogeneous, globular cluster, and nuclear star cluster flows are validated only at training points, yet the inference in Section 3 uses all five channels over a continuous range of χ_b (and α_CE for CE). Since biased interpolation in any channel enters the hierarchical likelihood and can shift both the inferred astrophysical parameters and the branching fractions, per-channel leave-one-out/cross-validation tests (with KL differences and uncertainties) are needed to support the statement in Section 3 that the flows are 'robust interpolators for a diverse range of population distributions.'
  2. [Section 2 (KL comparisons)] The quoted quantities have no uncertainties: −0.04 nat for the leave-one-out comparison, and −0.37 to −0.97 nat for flow-versus-KDE average differences. With finite samples, KL estimates are noisy; the estimator (e.g., number of samples, binning or k-NN method) is not described. Without repeated training seeds or bootstrap errors, the −0.04 nat difference cannot be distinguished from zero, and the KDE comparison may be on training data rather than independent test data. Please add uncertainties and specify the evaluation protocol.
  3. [Section 2 / Figure 1] The abstract says the paper measures branching ratios and evolution parameters, but the posterior numbers quoted in Section 2 are attributed to companion paper [28]. The hierarchical inference likelihood, selection-function model, priors, and branching-fraction definitions are not described. If the results are those of [28], the present paper should say so explicitly and be framed as a methods summary; if they are new here, the inference setup must be specified. This distinction matters for assessing the value added by this manuscript.
minor comments (5)
  1. [Section 1] Typo: 'the study of of massive stars' should read 'the study of massive stars'.
  2. [Figure 1] Top-right posterior panels: the y-axes ('p(χ_b)', 'p(α_CE)') have no scale; add tick labels and indicate the credible regions used for the quoted intervals.
  3. [Section 2] 'Predict p(θ|λ) at any χ_b and α_CE within the simulated range' should be qualified as 'within the convex hull of the training grid'; no extrapolation test is shown beyond the training values.
  4. [Section 2] The manuscript gives no architecture or training details for the flows (flow type, number of layers, learning rate, training-set size, normalization, etc.). Either add a table or point readers to the specific sections of [28].
  5. [Section 2] Define 'underlying' versus 'detected' branching fractions at first use; the distinction is important for interpreting the quoted values.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the interpolation claim is an empirical held-out test, not a definitional identity.

full rationale

The paper's central claim is that normalising flows trained on population-synthesis outputs can interpolate p(theta|lambda) at untrained (chi_b, alpha_CE) values. This is an empirical emulator claim, not a self-definitional one: the flow is a learned function of lambda, and the leave-one-out test (Section 2) removes one training lambda point and checks the flow against the held-out data. That is a genuine prediction step. The reported KL improvements over KDEs are in-sample fit comparisons, but the paper does not rename those fits as the headline interpolation prediction; it separately quotes a leave-one-out KL difference of -0.04 nat. The main inference results are attributed to the authors' companion paper [28], and the leave-one-out validation is also cited to [28]. This is heavy self-citation, but it is not circular: [28] is an earlier published paper containing the trained flows and validation, and the present paper quotes its numbers as evidence rather than defining them into existence. The lack of per-channel leave-one-out tests for the other four channels is a genuine generalizability/robustness concern, but absence of evidence is not circularity; it does not make the interpolation result equivalent to the training inputs by construction. No equation or fitted parameter is reused under a new name, and no uniqueness theorem or ansatz is imported from the authors' prior work to force the conclusion. Therefore the derivation chain is not circular, score 0.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced; the normalizing flows are a computational tool. The central inference depends on fitted population parameters (chi_b, alpha_CE, branching fractions) and on the accuracy of the flow emulator, which itself depends on network parameters and hyperparameters. The completeness of the five channels and the interpolation accuracy across all channels are domain assumptions that are only partially validated.

free parameters (5)
  • natal spin chi_b = 0.04+0.04-0.01 (90% posterior)
    Population parameter inferred from GWTC-3 observations using the flow emulator.
  • common-envelope efficiency alpha_CE = > 3.7 at 90% credibility
    Population parameter inferred from GWTC-3 observations.
  • branching fractions of five channels = CE channel 0.908+0.045-0.102; others not specified
    Relative weights of formation channels fitted to observations.
  • normalizing flow network weights = trained on population synthesis samples
    The emulator parameters are fitted to simulation data and determine the interpolated distributions used in inference.
  • flow hyperparameters (architecture, learning rate, etc.) = not reported; tuned with Weights and Biases [54]
    Choices affect emulator accuracy and are selected by optimization, not derived.
assumptions (4)
  • domain assumption The five selected population-synthesis channels (common envelope, stable mass transfer, chemically homogeneous evolution, globular clusters, nuclear star clusters) constitute a complete set of BBH formation channels
    Invoked in Section 2 when interpreting branching fractions; if a channel is missing, the inferred branching fractions are biased.
  • domain assumption The normalizing flow interpolation is smooth and accurate between training points over the entire lambda range
    Section 2 validates only one held-out point for the common-envelope channel; the inference assumes this holds for all channels and parameters.
  • domain assumption The GWTC-3 catalog and its selection function are correctly modeled
    Used in the hierarchical likelihood via the AMAZE framework [24, 28]; not re-derived here.
  • standard math KL divergence is an appropriate metric for comparing emulator and target distributions
    Section 2 uses KL divergence for performance comparison.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Exploring the astrophysical origins of binary black holes using normalising flows." pith.science (2026). https://pith.science/paper/WCUOIIH3

@misc{pith2026250819336,
  author       = {Pith},
  title        = {Pith review of: Exploring the astrophysical origins of binary black holes using normalising flows},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WCUOIIH3}},
  note         = {Machine review of arXiv:2508.19336}
}
read the original abstract

The growing number of gravitational-wave detections from binary black holes enables increasingly precise measurements of their population properties. The observed population is most likely drawn from multiple formation channels. Population-synthesis simulations allow detailed modelling of each of these channels, and comparing population-synthesis models with the observations allows us to constrain the uncertain physics of binary black hole formation and evolution. However, the most detailed population-synthesis codes are computationally expensive. We demonstrate the use of normalising flows to emulate five different population synthesis models, reducing the computational expense, and allowing interpolation between the populations predicted for different simulation inputs. With the trained normalising flows, we measure the branching ratios of different formation channels and details of binary stellar evolution, using the current catalogue of gravitational-wave observations.

Figures

Figures reproduced from arXiv: 2508.19336 by the authors.

Figure 1
Figure 1. Bottom left: The normalising-flow emulated distributions of chirp mass, mass ratio, effective inspiral spin and redshift for the common-envelope channel at five values of natal spin χb and common￾envelope efficiency αCE. The solid lines show the emulated distribution evaluated where there is training data from population synthesis. The dashed distributions are evaluated at {χb, αCE} where there is no training data, … view at source ↗

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

60 extracted references · 18 canonical work pages

  1. [28]

    J.988 189 (Preprint 2503.03819)

    Colloms S, Berry C P L, Veitch J and Zevin M 2025 Astrophys. J.988 189 (Preprint 2503.03819)

    arXiv 2025

  2. [1]

    Sana H, de Mink S E, de Koter A, Langer N, Evans C J, Gieles M, Gosset E, Izzard R G, Bouquin J B L and Schneider F R N 2012 Science 337 444 (Preprint 1207.6397)

    arXiv 2012

  3. [2]

    Marchant P and Bodensteiner J 2024 Ann. Rev. Astron. Astrophys.62 21–61 (Preprint 2311.01865)

    arXiv 2024

  4. [3]

    Duchˆ ene G and Kraus A 2013Ann. Rev. Astron. Astrophys.51 269 (Preprint 1303.3028)

    arXiv

  5. [4]

    Antonini F, Gieles M and Gualandris A 2019 Mon. Not. Roy. Astron. Soc.486 5008–5021 (Preprint 1811.03640)

    arXiv 2019

  6. [5]

    2021 Astron

    Bavera S S et al. 2021 Astron. Astrophys.647 A153 (Preprint 2010.16333)

    arXiv 2021

  7. [6]

    The Uncertain Future of Massive Binaries Obscures the Origin of LIGO/Virgo Sources

    Belczynski K, Romagnolo A, Olejak A, Klencki J, Chattopadhyay D, Stevenson S, Miller M C, Lasota J P and Crowther P A 2022 Astrophys. J.925 69 (Preprint 2108.10885)

    work page Pith review arXiv 2022

  8. [7]

    J.931 94 (Preprint 2204.13025)

    Fryer C L, Olejak A and Belczynski K 2022 Astrophys. J.931 94 (Preprint 2204.13025)

    arXiv 2022

Show all 60 references
  1. [8]

    J.987 164 (Preprint 2412.07831)

    Burrows A, Wang T and Vartanyan D 2025 Astrophys. J.987 164 (Preprint 2412.07831)

    2025 arXiv

  2. [9]

    Mapelli M 2021 Formation Channels of Single and Binary Stellar-Mass Black Holes(Springer) 1–65 (Preprint 2106.00699)

    2021 arXiv

  3. [10]

    (LIGO Scientific, Virgo, KAGRA) 2023 Phys

    Abbott R et al. (LIGO Scientific, Virgo, KAGRA) 2023 Phys. Rev. X 13 011048 ( Preprint 2111.03634)

    2023 arXiv

  4. [11]

    Di Carlo U N, Agrawal P, Rodriguez C L and Breivik K 2024 Astrophys. J. 965 22 ( Preprint 2306.13121)

    2024 arXiv

  5. [12]

    2025 Astron

    Xing Z et al. 2025 Astron. Astrophys.693 A27 (Preprint 2407.00200)

    2025 arXiv

  6. [13]

    Callister T A 2024 arXiv e-prints (Preprint 2410.19145)

    2024 arXiv

  7. [14]

    2025 Astron

    Willcox R et al. 2025 Astron. Astrophys.700 A59 (Preprint 2504.16669)

    2025 arXiv

  8. [15]

    (LIGO Scientific, Virgo) 2016 Astrophys

    Abbott B P et al. (LIGO Scientific, Virgo) 2016 Astrophys. J. Lett.818 L22 (Preprint 1602.03846)

    2016 arXiv

  9. [16]

    Fishbach M and Kalogera V 2021 Astrophys. J. Lett.914 L30 (Preprint 2105.06491)

    2021 arXiv

  10. [17]

    Eldridge J J, Stanway E R and Tang P N 2019 Mon. Not. Roy. Astron. Soc.482 870–880 (Preprint 1807.07659)

    2019 arXiv

  11. [18]

    2022 Astron

    Bavera S S et al. 2022 Astron. Astrophys.657 L8 (Preprint 2106.15841)

    2022 arXiv

  12. [19]

    Liotine C, Zevin M, Berry C P L, Doctor Z and Kalogera V 2023 Astrophys. J. 946 4 ( Preprint 2210.01825)

    2023 arXiv

  13. [20]

    Stevenson S, Vigna-G´ omez A, Mandel I, Barrett J W, Neijssel C J, Perkins D and de Mink S E 2017 Nature Commun.8 14906 (Preprint 1704.01352)

    2017 arXiv

  14. [21]

    Zevin M, Pankow C, Rodriguez C L, Sampson L, Chase E, Kalogera V and Rasio F A 2017Astrophys. J. 846 82 (Preprint 1704.07379)

    arXiv

  15. [22]

    Neijssel C J, Vigna-G´ omez A, Stevenson S, Barrett J W, Gaebel S M, Broekgaarden F, de Mink S E, Sz´ ecsi D, Vinciguerra S and Mandel I 2019 Mon. Not. Roy. Astron. Soc.490 3740–3759 (Preprint 1906.08136)

    2019 arXiv

  16. [23]

    Bouffanais Y, Mapelli M, Santoliquido F, Giacobbo N, Iorio G and Costa G 2021 Mon. Not. Roy. Astron. Soc.505 3873–3882 (Preprint 2010.11220)

    2021 arXiv

  17. [24]

    J.910 152 (Preprint 2011.10057)

    Zevin M, Bavera S S, Berry C P L, Kalogera V, Fragos T, Marchant P, Rodriguez C L, Antonini F, Holz D E and Pankow C 2021 Astrophys. J.910 152 (Preprint 2011.10057)

    2021 arXiv

  18. [25]

    Mastrogiovanni S, Lamberts A, Srinivasan R, Bruel T and Christensen N 2022 Mon. Not. Roy. Astron. Soc.517 3432–3444 (Preprint 2207.00374)

    2022 arXiv

  19. [26]

    Stevenson S and Clarke T A 2022 Mon. Not. Roy. Astron. Soc.517 4034–4053 (Preprint 2210.05040)

    2022 arXiv

  20. [27]

    Barrett J W, Gaebel S M, Neijssel C J, Vigna-G´ omez A, Stevenson S, Berry C P L, Farr W M and Mandel I 2018 Mon. Not. Roy. Astron. Soc.477 4685–4695 (Preprint 1711.06287)

    2018 arXiv

  21. [29]

    Breivik K 2025 arXiv e-prints (Preprint 2502.03523)

    2025 arXiv

  22. [30]

    2024 arXiv e-prints (Preprint 2411.02376)

    Andrews J J et al. 2024 arXiv e-prints (Preprint 2411.02376)

    2024 arXiv

  23. [31]

    Machine Learning Res.22 2617–2680 (Preprint 1912.02762)

    Papamakarios G, Nalisnick E, Rezende D J, Mohamed S and Lakshminarayanan B 2021 J. Machine Learning Res.22 2617–2680 (Preprint 1912.02762)

    2021 arXiv

  24. [32]

    Pattern Anal

    Kobyzev I, Prince S J D and Brubaker M A 2021 IEEE Trans. Pattern Anal. Machine Intell.43 3964–3979 (Preprint 1908.09257)

    2021 arXiv

  25. [33]

    Wong K W K, Contardo G and Ho S 2020 Phys. Rev. D101 123005 (Preprint 2002.09491)

    2020 arXiv

  26. [34]

    Paczynski B 1976 Symposium - International Astronomical Union73 75

    1976

  27. [35]

    van den Heuvel E P J 1976 Late Stages of Close Binary Systems Structure and Evolution of Close Binary Systems vol 73 ed Eggleton P, Mitton S and Whelan J p 35

    1976

  28. [36]

    J.759 52 (Preprint 1202.4901)

    Dominik M, Belczynski K, Fryer C, Holz D, Berti E, Bulik T, Mandel I and O’Shaughnessy R 2012 Astrophys. J.759 52 (Preprint 1202.4901)

    2012 arXiv

  29. [37]

    2013 Astron

    Ivanova N et al. 2013 Astron. Astrophys. Rev.21 59 (Preprint 1209.4302)

    2013 arXiv

  30. [38]

    van den Heuvel E P J, Portegies Zwart S F and de Mink S E 2017 Mon. Not. Roy. Astron. Soc.471 4256–4264 (Preprint 1701.02355)

    2017 arXiv

  31. [39]

    J.922 110 (Preprint 2107.05702)

    Gallegos-Garcia M, Berry C P L, Marchant P and Kalogera V 2021 Astrophys. J.922 110 (Preprint 2107.05702)

    2021 arXiv

  32. [40]

    J.931 17 (Preprint 2110.01634)

    van Son L A C, de Mink S E, Callister T, Justham S, Renzo M, Wagg T, Broekgaarden F S, Kummer F, Pakmor R and Mandel I 2022 Astrophys. J.931 17 (Preprint 2110.01634)

    2022 arXiv

  33. [41]

    Briel M M, Stevance H F and Eldridge J J 2023Mon. Not. Roy. Astron. Soc.520 5724–5745 (Preprint 2206.13842)

    arXiv

  34. [42]

    252 365–370 (Preprint 0805.2544)

    de Mink S E, Cantiello M, Langer N, Yoon S C, Brott I, Glebbeek E, Verkoulen M and Pols O R 2008 IAU Symp. 252 365–370 (Preprint 0805.2544)

    2008 arXiv

  35. [43]

    Mandel I and de Mink S E 2016 Mon. Not. Roy. Astron. Soc.458 2634–2647 (Preprint 1601.00007)

    2016 arXiv

  36. [44]

    du Buisson L, Marchant P, Podsiadlowski P, Kobayashi C, Abdalla F B, Taylor P, Mandel I, de Mink S E, Moriya T J and Langer N 2020 Mon. Not. Roy. Astron. Soc.499 5941–5959 (Preprint 2002.11630)

    2020 arXiv

  37. [45]

    Heggie D C 1975 Mon. Not. Roy. Astron. Soc.173 729–787

    1975

  38. [46]

    Fitchett M J 1983 Mon. Not. Roy. Astron. Soc.203 1049–1062

    1983

  39. [47]

    J.831 187 (Preprint 1606.04889)

    Antonini F and Rasio F A 2016 Astrophys. J.831 187 (Preprint 1606.04889)

    2016 arXiv

  40. [48]

    Rodriguez C L, Zevin M, Amaro-Seoane P, Chatterjee S, Kremer K, Rasio F A and Ye C S 2019 Phys. Rev. D100 043027 (Preprint 1906.10260)

    2019 arXiv

  41. [49]

    (LIGO Scientific, Virgo, KAGRA) 2023 Phys

    Abbott R et al. (LIGO Scientific, Virgo, KAGRA) 2023 Phys. Rev. X 13 041039 ( Preprint 2111.03606)

    2023 arXiv

  42. [50]

    Dewancker I, McCourt M and Clark S 2016 arXiv e-prints (Preprint 1612.04858)

    2016 arXiv

  43. [51]

    Zhang X, Chen X, Yao L, Ge C and Dong M 2019 Deep neural network hyperparameter optimization with orthogonal array tuning International conference on neural information processing(Springer) 287–295

    2019

  44. [52]

    Koehler F, Mehta V and Risteski A 2021 Representational aspects of depth and conditioning in normalizing flows Proceedings of the 38th International Conference on Machine Learning(Proceed- ings of Machine Learning Researchvol 139) ed Meila M and Zhang T (PMLR) 5628–5636 URL ht...

    2021

  45. [53]

    Jiang C, Huang Z, Pedapati T, Chen P Y, Sun Y and Gao J 2024 Nature Commun.15 5718

    2024

  46. [54]

    Biewald L 2020 Experiment tracking with weights and biases www.wandb.com

    2020

  47. [55]

    Kullback S and Leibler R A 1951 The Annals of Mathematical Statistics22 79–86

    1951

  48. [56]

    Iaconi R and De Marco O 2019 Mon. Not. Roy. Astron. Soc.490 2550–2566 (Preprint 1902.02039)

    2019 arXiv

  49. [57]

    2020 arXiv e-prints (Preprint 2011.06630)

    Law-Smith J A P et al. 2020 arXiv e-prints (Preprint 2011.06630)

    2020 arXiv

  50. [58]

    Lau M Y M, Hirai R, Gonz´ alez-Bol ´ ıvar M, Price D J, De Marco O and Mandel I 2022 Mon. Not. Roy. Astron. Soc.512 5462–5480 (Preprint 2111.00923)

    2022 arXiv

  51. [59]

    Astrophys.667 A72 (Preprint 2111.12112)

    Moreno M M, Schneider F R N, Roepke F K, Ohlmann S T, Pakmor R, Podsiadlowski P and Sand C 2022 Astron. Astrophys.667 A72 (Preprint 2111.12112)

    2022 arXiv

  52. [60]

    Roepke F K and De Marco O 2023 Liv. Rev. Comput. Astrophys.9 2 (Preprint 2212.07308)

    2023 arXiv

Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.