Pith. sign in

REVIEW 3 major objections 7 minor 134 references

Emulating only the relativistic reflection spectrum yields O(0.1)% accuracy and recovers true black-hole parameters without the posterior bias of full-model surrogates.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · grok-4.5

2026-07-11 13:32 UTC pith:4N7W3WDE

load-bearing objection Solid modular emulator that mostly fixes the prior bias problem, but the abstract over-sells “unbiased recovery” given a clear spin offset in the only MCMC test. the 3 major comments →

arxiv 2607.04785 v1 pith:4N7W3WDE submitted 2026-07-06 astro-ph.IM astro-ph.HE

Emulation of non-linear 1D spectral models: relativistic X-ray reflection

Benjamin J. Ricketts , Tin Had\v{z}i Veljkovi\'c , Daniela Huppenkothen , Adam Ingram , Matteo Lucchini , Guglielmo Mastroserio , Fergus J. E. Baker This is my paper
classification astro-ph.IM astro-ph.HE
keywords machine learningblack holesemulationX-ray reflectionoperator learningspectral modelsreltrans
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.

The paper argues that whether and how to emulate a complex numerical spectrum should follow from a systematic look at how that spectrum actually varies with each physical parameter. For the black-hole X-ray model reltrans, the expensive non-linear piece is the relativistically smeared reflection spectrum, which is only 1–10% of the total flux. By training an operator-learning network solely on that component—using Fourier features of energy, FiLM conditioning on the ten physical parameters, a power-law trend head, and a weak derivative regulariser—the authors obtain RTFAST2, which matches the true reflection spectrum to roughly 0.1% across 0.1–100 keV and is 4–10 times faster (with larger gains under vectorised evaluation). When the emulator is dropped into a Bayesian fit of a simulated NuSTAR observation, the recovered posteriors contain the true parameters and lack the systematic offsets that plagued their earlier end-to-end emulator. The broader claim is that no single architecture transfers across models; successful surrogates must be designed around the structure of the target physics, and modular emulation of only the expensive sub-component is a practical route to that design.

Core claim

A modular operator-learning emulator that maps continuous energy and ten physical parameters to the relativistically convolved reflection spectrum of reltrans recovers that spectrum to O(0.1)% precision over 0.1–100 keV, delivers a 4–10 imes speed-up, and, when used inside MCMC, recovers the true parameters of a simulated observation without the systematic posterior biases of the authors’ previous full-model emulator.

What carries the argument

RTFAST2: an operator-learning network that evaluates the reflection spectrum as a continuous function of energy, with random Fourier features of the energy coordinate, FiLM layers that condition residual blocks on the physical parameters, an optional power-law trend head, relative-error loss, and a weak Sobolev regulariser.

Load-bearing premise

That one carefully chosen simulated NuSTAR spectrum, trained on Latin-hypercube samples and fitted with tight priors around truth, is enough to claim that the emulator introduces no systematic posterior bias for real observations.

What would settle it

Run the same MCMC pipeline on a real NuSTAR (or multi-instrument) spectrum whose parameters are independently known, or on an ensemble of simulations that deliberately stress the residual iron-line spike and high-energy error growth; if the recovered posteriors are systematically offset from truth or from the original reltrans chain, the no-bias claim fails.

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

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 / 7 minor

Summary. The paper presents RTFAST2, a modular neural emulator for the relativistically convolved reflection spectrum of the black-hole X-ray model reltrans (rather than the full spectrum). After a diagnostic characterisation of how the spectrum varies with individual parameters, the authors train an operator-learning network with random Fourier feature embeddings of energy, FiLM conditioning on physical parameters, a power-law trend head, a relative-error (Huber) loss, and a weak Sobolev regulariser. On a Latin-hypercube test set they report that ~85% of spectra achieve mean relative error ≤1% (and nearly all ≤10%) over 0.1–100 keV, with a 4–10× wall-clock speed-up that improves under vectorisation. Ablations (Table 4) and capacity/data scaling (Table 5) support the architectural choices. A single NuSTAR-like simulated observation is used for MCMC recovery; most free parameters are recovered near truth, improving on the confident-but-biased posteriors of their previous end-to-end emulator (BR25).

Significance. Computational cost of relativistic reflection models is a genuine bottleneck for Bayesian inference on large X-ray datasets. The modular strategy—emulating only the expensive, low-flux reflection component while retaining analytic continuum and absorption—is a clear methodological contribution and is well motivated by the model structure. Operator learning with Fourier features and FiLM is appropriately chosen for high-frequency, parameter-dependent spectral features, and the paper supplies ablations, residual maps, chi-squared slices, public data/code, and an explicit argument against universal architectures. If the precision and bias claims hold under broader validation, RTFAST2 would be a practically useful drop-in for xspec-compatible workflows and a useful template for other expensive spectral modules.

major comments (3)
  1. Abstract and §4 claim that RTFAST2 “recovers the true parameters of simulated observations without the systematic posterior biases of our previous work.” Fig. 5 shows spin recovered at a = 0.69 ± 0.02 versus truth a = 0.8 (~5σ under the reported 1-D width), with inclination also pulled low, despite truncated-Gaussian priors of FWHM 20% centred on truth and an extra flat 0.5% systematic. The authors note the iron-line residual spike (Fig. 4) and spin–inclination degeneracy, but the abstract wording still overstates the result. Either temper the claim to “substantially reduced bias relative to BR25 / most parameters recovered” or add further simulated recoveries (different instruments, broader priors, free continuum) that demonstrate the spin offset is not systematic.
  2. Precision language is inconsistent and slightly overstated. The abstract states “O(0.1)% precision,” while §6 and the threshold metrics (Table 4: 85% of test spectra with mean ε_rel ≤ 0.01; residual map Fig. 4 with few-percent iron-line spikes and high-E growth) support O(1%) as the honest summary. Please align abstract, conclusions, and reported metrics, and quote mean/median relative error (not only threshold yields) so readers can judge fitness for percent-level systematics.
  3. Inference validation rests on a single simulated NuSTAR spectrum (Table 6, §4) with informative priors centred on truth. Because reflection is only ~1–10% of the total flux, residual shape errors near 6.4 keV can shift spin/inclination at the level of the statistical uncertainty once the continuum is free. At least a small suite of recoveries (varied spin, inclination, Γ, exposure, and prior width) is needed to support a general “no systematic posterior bias” statement; otherwise restrict the claim to the demonstrated case and BR25 comparison.
minor comments (7)
  1. Table 1 / Table 6 notation: R_inner appears twice in Table 6 with values -1 and 400; clarify which is log-space ISCO units vs outer radius, and keep symbols consistent with Table 1.
  2. §3.1.5 / Eq. (6): the expression for ε_rel mixes ŷ and 10^{ℓ̂-ℓ}; write the linear-space relative error explicitly in terms of predicted and true log-flux to avoid ambiguity.
  3. Fig. 3 bottom panel: the caption says “A value of 1 corresponds to a 1% offset” while the axis is labelled “% Difference”; make units and zero-point consistent.
  4. Appendix C figures still label the emulator “rtfast” rather than RTFAST2; update for clarity relative to BR25.
  5. §2.2 filter (Γ>2.75, log ξ>4, log N_e>17 excluded): state briefly how often real fits enter this regime and whether users should fall back to the numerical model there.
  6. Speed-up: quote absolute evaluation times (CPU/GPU, batch size) for reltrans vs RTFAST2 so the 4–10× factor and vectorisation gains can be reproduced.
  7. Typos / style: “Theuseofmachinelearning…”, “astronomicalsurrogatemodelling”, missing spaces after periods in several places (likely PDF line-break artefacts); a careful copy-edit pass would help.

Circularity Check

0 steps flagged

No circularity: emulator is trained and validated against independent numerical ground truth from reltrans; parameter recovery is a direct test, not a redefinition of fitted inputs.

full rationale

The paper's chain is self-contained and non-circular. Training spectra are generated from the external numerical code reltransDCp (Latin-hypercube sampling over the parameter ranges in Table 1, fixed parameters in Table 2). The network (operator learning + RFF + FiLM + trend head + relative-error loss + weak Sobolev regulariser) is fitted to approximate those spectra; held-out test metrics (Tables 4–5, Figs. 3–4) and the single MCMC recovery experiment (Table 6 parameters, NuSTAR-like simulation, Fig. 5) are evaluated against the same independent ground truth. Self-citation of BR25/RTFAST is used only as a performance baseline that the new modular emulator improves upon; it does not supply any uniqueness theorem, ansatz, or load-bearing premise that forces the present results. No quantity is defined in terms of the quantity it is claimed to predict, no fitted coefficient is renamed a prediction, and no known empirical pattern is merely re-labelled. Residual biases (e.g., the mild spin offset) are empirical shortcomings of the approximation, not circular reductions. Score 0 is therefore the correct finding.

Axiom & Free-Parameter Ledger

5 free parameters · 4 axioms · 1 invented entities

The central performance claims rest on the numerical fidelity of reltrans v2.3.1, the Latin-hypercube coverage of the 10-dimensional parameter space (with an ad-hoc filter), the chosen network capacity and loss weights, and the assumption that one simulated observation plus residual diagnostics generalize. No new physical entities are postulated; free parameters are standard ML hyper-parameters and training-set design choices.

free parameters (5)
  • Sobolev regularizer weight λ
    Set to O(10^{-3}); controls smoothness vs pointwise fit and is chosen by hand rather than derived.
  • Huber δ = 0.05
    Threshold in the relative-error loss; selected for training stability.
  • Network width/depth (6 FiLM-MLP blocks, d=376, 256 RFF bands, ~8 M parameters)
    Final capacity chosen after scaling experiments; saturates performance but is not uniquely determined by theory.
  • Latin-hypercube sample size (1.5 M spectra) and 90/10 splits
    Training volume and split ratios are design choices that directly set the reported yield percentages.
  • Parameter-space filter (Γ>2.75, log ξ>4, log Ne>17 excluded)
    Ad-hoc exclusion of regions where xillver loses iron lines; affects the domain over which the O(0.1)% claim holds.
axioms (4)
  • domain assumption reltrans v2.3.1 (with the Fourier-convolution fix of App. A) is an accurate ground-truth generator of reflection spectra
    All training labels and residual diagnostics are defined relative to this numerical model.
  • domain assumption The continuum (nthcomp) and absorption can be applied analytically after the reflection emulator
    Justifies the modular strategy that only 1–10% of the flux needs high-fidelity emulation.
  • standard math Operator learning + random Fourier features can represent both smooth continua and narrow relativistic lines to the required precision
    Invoked via Tancik et al. (2020) and the architecture of §3.1; supported by ablations but not proved for this spectrum family.
  • ad hoc to paper Latin-hypercube sampling with the listed priors adequately covers the scientifically relevant volume
    No coverage diagnostics beyond the final test-set yields are provided.
invented entities (1)
  • RTFAST2 emulator independent evidence
    purpose: Drop-in surrogate for the relativistically convolved reflection spectrum inside reltrans
    The trained network itself; independent evidence is the public code and residual statistics against the original model.

pith-pipeline@v1.1.0-grok45 · 26641 in / 2788 out tokens · 25867 ms · 2026-07-11T13:32:02.829592+00:00 · methodology

0 comments
read the original abstract

The use of machine learning techniques to approximate computationally expensive models has become increasingly prevalent in a wide variety of fields within astronomy. We discuss the implementation of emulators for 1-dimensional models in the context of the astrophysical numerical model reltrans, a black hole X-ray spectral model that models the effects of relativistically smeared emission from an accretion disk. We argue that the decision of whether and how to emulate should follow from a systematic characterisation of the target model, and we demonstrate a diagnostic workflow: examining how the spectrum varies with individual parameters. We adopt a modular strategy, emulating only the relativistically convolved reflection spectrum (1-10% of the total flux) rather than the full model. Using an operator-learning architecture with Fourier feature embeddings and FiLM conditioning, we reproduce the reflection spectrum to O(0.1)% precision across 0.1-100 keV with a 4-10x speed-up that scales considerably better under vectorised evaluation. This emulator, RTFAST2, recovers the true parameters of simulated observations without the systematic posterior biases of our previous work. We conclude that no architecture is universally transferable and bespoke emulators motivated by a model's specific structure are required. The modular approach taken in this work presents a promising strategy for future emulators of numerical models.

Figures

Figures reproduced from arXiv: 2607.04785 by Adam Ingram, Benjamin J. Ricketts, Daniela Huppenkothen, Fergus J. E. Baker, Guglielmo Mastroserio, Matteo Lucchini, Tin Had\v{z}i Veljkovi\'c.

Figure 1
Figure 1. Figure 1: Left: the reflection spectrum coloured as a function of how far the inner-most radius of the disk extends. Dark blue indicates smaller truncation of the disk and more reflection and relativistic effects, bright yellow indicates larger truncation and less reflection and relativistic effects. Right: the reflection spectrum coloured as a function of inclination of the disk in respect to the observer. The larg… view at source ↗
Figure 2
Figure 2. Figure 2: Visualisation of the emulator architecture. Input blocks are plotted in blue, featurizing blocks are plotted in orange, FiLM-MLP blocks are coloured in green, the head blocks (trend-heads and end of FiLM-MLP blocks) are plotted in purple, and the output spectrum block is plotted in red. The shape of the input shape of each block is shown below the block. B indicates the batch size, L indicates the length o… view at source ↗
Figure 3
Figure 3. Figure 3: Top panel: the reltrans (blue solid) and RTFAST2 (orange dashed) spectra in 𝑘𝑒𝑉/𝑐𝑚2 /𝑠 units. Bottom panel: The fractional difference between RTFAST2 and reltrans. A value of 1 corresponds to a 1% offset of the emulated spectrum compared to the original reltrans value. Model Size Yield (%) (Parameters) 𝜖rel ≤ 0.01 𝜖rel ≤ 0.10 16K 49.77 93.49 512K 75.47 99.90 8M 85.24 99.90 32M 85.02 99.90 [PITH_FULL_IMAGE… view at source ↗
Figure 4
Figure 4. Figure 4: Distribution of the percentage residual difference between RTFAST2 and reltrans as a function of energy. The shade of region indicates the 25 − 75%, 5 − 95%, and 1 − 99% region in increasing lightness respectively. ture choices affect bias in our emulation. We plot the distribution of percentage residuals between reltrans and RTFAST2 in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Posterior plots created using RTFAST2 on simulated reltrans data. The true parameters are plotted with a solid blue line and the dashed lines in the diagonal 1-dimensional histogram plots show the 1-sigma and median quantiles of the 1-dimensional posteriors. squared between the emulator and original model in Appendix C better reflects the capability of the emulator in this case. 5 DISCUSSION We have design… view at source ↗
Figure 6
Figure 6. Figure 6: Top panel: Plot of the distribution of 200 model evaluations drawn from the posterior, compared to the simulated data. A zoomed in-set panel shows the posteriors draw distribution about the relativistic Fe-K line. While we plot the 25 − 75% (dark blue shaded) and 2.5 − 97.5% (light blue shaded) bands as filled in bands, they are not visible to the naked eye in the full plot and are tightly distributed in t… view at source ↗

discussion (0)

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

Reference graph

Works this paper leans on

134 extracted references · 9 canonical work pages · 8 internal anchors

  1. [1]

    ApJ , fjournal=

    Fournier, Paul , title=. ApJ , fjournal=

  2. [2]

    An important paper , journal=

  3. [3]

    Another Unreal Paper , journal=

  4. [4]

    A Last Unreal Paper , journal=

  5. [5]

    , keywords =

    X-ray fluorescence from the inner disc in Cygnus X-1. , keywords =. doi:10.1093/mnras/238.3.729 , adsurl =

    doi:10.1093/mnras/238.3.729

  6. [6]

    Monthly Notices of the Royal Astronomical Society , volume=

    On measuring the Hubble constant with X-ray reverberation mapping of active galactic nuclei , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2022 , publisher=

    2022

  7. [7]

    The European Physical Journal C , volume=

    Constraining the parameters of high-dimensional models with active learning , author=. The European Physical Journal C , volume=. 2019 , publisher=

    2019

  8. [8]

    The Astrophysical Journal Supplement Series , volume=

    SPECULATOR: Emulating stellar population synthesis for fast and accurate galaxy spectra and photometry , author=. The Astrophysical Journal Supplement Series , volume=. 2020 , publisher=

    2020

  9. [9]

    arXiv preprint arXiv:1511.06412 , year=

    Qbdc: query by dropout committee for training deep supervised architecture , author=. arXiv preprint arXiv:1511.06412 , year=

    Pith/arXiv arXiv

  10. [10]

    The Astrophysical Journal Letters , volume=

    Dalek: A Deep Learning Emulator for TARDIS , author=. The Astrophysical Journal Letters , volume=. 2021 , publisher=

    2021

  11. [11]

    Comprehensive Review of Artificial Neural Network Applications to Pattern Recognition , year=

    Abiodun, Oludare Isaac and Jantan, Aman and Omolara, Abiodun Esther and Dada, Kemi Victoria and Umar, Abubakar Malah and Linus, Okafor Uchenwa and Arshad, Humaira and Kazaure, Abdullahi Aminu and Gana, Usman and Kiru, Muhammad Ubale , journal=. Comprehensive Review of Artificial Neural Network Applications to Pattern Recognition , year=

  12. [12]

    The Astrophysical Journal , volume=

    Reverberation mapping of the Kepler field AGN KA1858+ 4850 , author=. The Astrophysical Journal , volume=. 2014 , publisher=

    2014

  13. [13]

    Monthly Notices of the Royal Astronomical Society , volume=

    Photometric redshifts for the SDSS Data Release 12 , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2016 , publisher=

    2016

  14. [14]

    Curran Associates, Inc , pages=

    Advances in neural information processing systems 32 , author=. Curran Associates, Inc , pages=

  15. [15]

    Technometrics , volume=

    A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , author=. Technometrics , volume=. 2000 , publisher=

    2000

  16. [16]

    arXiv preprint arXiv:1606.08415 , year=

    Gaussian error linear units (gelus) , author=. arXiv preprint arXiv:1606.08415 , year=

    Pith/arXiv arXiv

  17. [17]

    Results in Physics , volume=

    The imaging x-ray polarimetry explorer (IXPE) , author=. Results in Physics , volume=. 2016 , publisher=

    2016

  18. [18]

    Space Telescopes and Instrumentation 2012: Ultraviolet to Gamma Ray , volume=

    The Neutron star Interior Composition ExploreR (NICER): an Explorer mission of opportunity for soft x-ray timing spectroscopy , author=. Space Telescopes and Instrumentation 2012: Ultraviolet to Gamma Ray , volume=. 2012 , organization=

    2012

  19. [19]

    The spacecraft and operations , author=

    XMM-Newton observatory-I. The spacecraft and operations , author=. Astronomy & Astrophysics , volume=. 2001 , publisher=

    2001

  20. [20]

    X-ray properties of black-hole binaries , author=. Annu. Rev. Astron. Astrophys. , volume=. 2006 , publisher=

    2006

  21. [21]

    Monthly Notices of the Royal Astronomical Society , volume=

    A public relativistic transfer function model for X-ray reverberation mapping of accreting black holes , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2019 , publisher=

    2019

  22. [22]

    The Astrophysical Journal , volume=

    On the absorption of X-rays in the interstellar medium , author=. The Astrophysical Journal , volume=. 2000 , publisher=

    2000

  23. [23]

    X-ray reflected spectra from accretion disk models. III. A complete grid of ionized reflection calculations , author=. The Astrophysical Journal , volume=. 2013 , publisher=

    2013

  24. [24]

    Reviews of Modern Physics , volume=

    Atomic data for x-ray astrophysics , author=. Reviews of Modern Physics , volume=. 2007 , publisher=

    2007

  25. [25]

    Statistic Surveys , volume=

    Nested sampling methods , author=. Statistic Surveys , volume=. 2023 , publisher=

    2023

  26. [26]

    Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=

    Riemann manifold langevin and hamiltonian monte carlo methods , author=. Journal of the Royal Statistical Society Series B: Statistical Methodology , volume=. 2011 , publisher=

    2011

  27. [27]

    Proceedings of the National Academy of Sciences , volume=

    The frontier of simulation-based inference , author=. Proceedings of the National Academy of Sciences , volume=. 2020 , publisher=

    2020

  28. [28]

    Remote Sensing , volume=

    An emulator toolbox to approximate radiative transfer models with statistical learning , author=. Remote Sensing , volume=. 2015 , publisher=

    2015

  29. [29]

    The Astrophysical Journal , volume=

    Cosmic emulation: fast predictions for the galaxy power spectrum , author=. The Astrophysical Journal , volume=. 2015 , publisher=

    2015

  30. [30]

    Astronomische Nachrichten , volume=

    Relativistic reflection: Review and recent developments in modeling , author=. Astronomische Nachrichten , volume=. 2016 , publisher=

    2016

  31. [31]

    Monthly Notices of the Royal Astronomical Society , volume=

    dynesty: a dynamic nested sampling package for estimating Bayesian posteriors and evidences , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2020 , publisher=

    2020

  32. [32]

    Bayesian inference and maximum entropy methods in science and engineering , volume=

    Nested sampling , author=. Bayesian inference and maximum entropy methods in science and engineering , volume=

  33. [33]

    Astronomical Data Analysis , volume=

    Sherpa: a mission-independent data analysis application , author=. Astronomical Data Analysis , volume=. 2001 , organization=

    2001

  34. [34]

    Journal of Physics G: Nuclear and Particle Physics , volume=

    Extrapolating from neural network models: a cautionary tale , author=. Journal of Physics G: Nuclear and Particle Physics , volume=. 2021 , publisher=

    2021

  35. [35]

    Astrophysical Journal, Vol

    The optical appearance of a star orbiting an extreme Kerr black hole , author=. Astrophysical Journal, Vol. 183, pp. 237-264 (1973) , volume=

    1973

  36. [36]

    Astronomy & Astrophysics , volume=

    Radiation transfer of emission lines in curved space-time , author=. Astronomy & Astrophysics , volume=. 2004 , publisher=

    2004

  37. [37]

    Classical and Quantum Gravity , volume=

    GYOTO: a new general relativistic ray-tracing code , author=. Classical and Quantum Gravity , volume=. 2011 , publisher=

    2011

  38. [38]

    Monthly Notices of the Royal Astronomical Society , volume=

    A new emulated Monte Carlo radiative transfer disc-wind model: X-Ray Accretion Disc-wind Emulator--XRADE , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2022 , publisher=

    2022

  39. [39]

    Reliable Computing , volume=

    Universal approximation theorem for interval neural networks , author=. Reliable Computing , volume=. 1998 , publisher=

    1998

  40. [40]

    Computer , volume=

    Artificial neural networks: A tutorial , author=. Computer , volume=. 1996 , publisher=

    1996

  41. [41]

    The coyote universe. II. Cosmological models and precision emulation of the nonlinear matter power spectrum , author=. The Astrophysical Journal , volume=. 2009 , publisher=

    2009

  42. [42]

    The Astrophysical Journal , volume=

    NECOLA: toward a universal field-level cosmological emulator , author=. The Astrophysical Journal , volume=. 2022 , publisher=

    2022

  43. [43]

    Monthly Notices of the Royal Astronomical Society , volume=

    A theory of the instability of disk accretion on to black holes and the variability of binary X-ray sources, galactic nuclei and quasars , author=. Monthly Notices of the Royal Astronomical Society , volume=. 1976 , publisher=

    1976

  44. [44]

    Nature , volume=

    The corona contracts in a black-hole transient , author=. Nature , volume=. 2019 , publisher=

    2019

  45. [45]

    Monthly Notices of the Royal Astronomical Society , volume=

    General relativistic magnetohydrodynamic simulations of the jet formation and large-scale propagation from black hole accretion systems , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2006 , publisher=

    2006

  46. [46]

    Magnetically driven accretion in the Kerr metric. III. Unbound outflows , author=. The Astrophysical Journal , volume=. 2005 , publisher=

    2005

  47. [47]

    The astrophysical journal , volume=

    A measurement of the electromagnetic luminosity of a Kerr black hole , author=. The astrophysical journal , volume=. 2004 , publisher=

    2004

  48. [48]

    Monthly Notices of the Royal Astronomical Society , volume=

    CosmoPower: emulating cosmological power spectra for accelerated Bayesian inference from next-generation surveys , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2022 , publisher=

    2022

  49. [49]

    The Astrophysical Journal , volume=

    The coyote universe extended: precision emulation of the matter power spectrum , author=. The Astrophysical Journal , volume=. 2013 , publisher=

    2013

  50. [50]

    Journal of Cosmology and Astroparticle Physics , volume=

    An emulator for the Lyman- forest , author=. Journal of Cosmology and Astroparticle Physics , volume=. 2019 , publisher=

    2019

  51. [51]

    The Astrophysical Journal Letters , volume=

    Tearing up the disk: how black holes accrete , author=. The Astrophysical Journal Letters , volume=. 2012 , publisher=

    2012

  52. [52]

    Monthly Notices of the Royal Astronomical Society , volume=

    On the different flavours of Lense--Thirring precession around accreting stellar mass black holes , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2018 , publisher=

    2018

  53. [53]

    science , volume=

    Dynamic programming , author=. science , volume=. 1966 , publisher=

    1966

  54. [54]

    Monthly Notices of the Royal Astronomical Society , volume=

    Modelling correlated variability in accreting black holes: the effect of high density and variable ionization on reverberation lags , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2021 , publisher=

    2021

  55. [55]

    Monthly Notices of the Royal Astronomical Society , volume=

    Exploring the radial disc ionization profile of the black hole X-ray binary GRS 1915+ 105 , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2020 , publisher=

    1915

  56. [56]

    Observational appearance

    Black holes in binary systems. Observational appearance. , author=. Astronomy and Astrophysics, Vol. 24, p. 337-355 , volume=

  57. [57]

    The Astrophysical Journal , volume=

    NICER--NuSTAR observations of the neutron star low-mass x-ray binary 4u 1735--44 , author=. The Astrophysical Journal , volume=. 2020 , publisher=

    2020

  58. [58]

    The Astrophysical Journal , volume=

    Reflection Spectroscopy of the Black Hole Binary XTE J1752- 223 in Its Long-stable Hard State , author=. The Astrophysical Journal , volume=. 2018 , publisher=

    2018

  59. [59]

    Monthly Notices of the Royal Astronomical Society , volume=

    The spin measurement of the black hole in 4U 1543-47 constrained with the X-ray reflected emission , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2020 , publisher=

    2020

  60. [60]

    The Astrophysical Journal , volume=

    Measurements of the Hubble constant: tensions in perspective , author=. The Astrophysical Journal , volume=. 2021 , publisher=

    2021

  61. [61]

    Astronomy & Astrophysics , volume=

    Statistical evaluation of the flux cross-calibration of the XMM-Newton EPIC cameras , author=. Astronomy & Astrophysics , volume=. 2009 , publisher=

    2009

  62. [62]

    Monthly Notices of the Royal Astronomical Society , volume=

    Discovery of high-frequency iron K lags in Ark 564 and Mrk 335 , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2013 , publisher=

    2013

  63. [63]

    Monthly Notices of the Royal Astronomical Society , volume=

    A global look at X-ray time lags in Seyfert galaxies , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2016 , publisher=

    2016

  64. [64]

    Monthly Notices of the Royal Astronomical Society , volume=

    Investigating the hard state of MAXI J1820+ 070: a comprehensive Bayesian approach to black hole spin and accretion properties , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2024 , publisher=

    2024

  65. [65]

    Astronomy & Astrophysics , volume=

    X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue , author=. Astronomy & Astrophysics , volume=. 2014 , publisher=

    2014

  66. [66]

    Engineering Applications of Artificial Intelligence , volume=

    Ensemble deep learning: A review , author=. Engineering Applications of Artificial Intelligence , volume=. 2022 , publisher=

    2022

  67. [67]

    Renewable and Sustainable Energy Reviews , volume=

    Ensemble methods for wind and solar power forecasting—A state-of-the-art review , author=. Renewable and Sustainable Energy Reviews , volume=. 2015 , publisher=

    2015

  68. [68]

    Acm computing surveys (csur) , volume=

    Ensemble approaches for regression: A survey , author=. Acm computing surveys (csur) , volume=. 2012 , publisher=

    2012

  69. [69]

    Advances in neural information processing systems , volume=

    Simple and scalable predictive uncertainty estimation using deep ensembles , author=. Advances in neural information processing systems , volume=

  70. [70]

    Monthly Notices of the Royal Astronomical Society , volume=

    Broad-band -ray and X-ray spectra of NGC 4151 and their implications for physical processes and geometry , author=. Monthly Notices of the Royal Astronomical Society , volume=. 1996 , publisher=

    1996

  71. [71]

    Space Science Reviews , volume=

    Multi-Wavelength Variability: Accretion and Ejection at the Fastest Timescales , author=. Space Science Reviews , volume=. 2014 , publisher=

    2014

  72. [72]

    Astrophysical Journal, vol

    Cygnus X-1-an interpretation of the spectrum and its variability , author=. Astrophysical Journal, vol. 195, Feb. 1, 1975, pt. 2, p. L101-L105. , volume=

    1975

  73. [73]

    Nature , volume=

    Hard X-ray spectrum of CYG X-1 , author=. Nature , volume=. 1979 , publisher=

    1979

  74. [74]

    Space Science Reviews , volume=

    Relativistic jets in active galactic nuclei and microquasars , author=. Space Science Reviews , volume=. 2017 , publisher=

    2017

  75. [75]

    Astrophysical Journal, Part 1, vol

    Relativistic jets as compact radio sources , author=. Astrophysical Journal, Part 1, vol. 232, Aug. 15, 1979, p. 34-48. , volume=

    1979

  76. [76]

    The Astrophysical Journal , volume=

    On the jets associated with galactic superluminal sources , author=. The Astrophysical Journal , volume=. 1996 , publisher=

    1996

  77. [77]

    Monthly Notices of the Royal Astronomical Society , volume=

    Irradiation of an accretion disc by a jet: general properties and implications for spin measurements of black holes , author=. Monthly Notices of the Royal Astronomical Society , volume=. 2013 , publisher=

    2013

  78. [78]

    Technometrics , volume=

    Diagnostics for Gaussian process emulators , author=. Technometrics , volume=. 2009 , publisher=

    2009

  79. [79]

    The Planetary Science Journal , volume=

    Accurate machine-learning atmospheric retrieval via a neural-network surrogate model for radiative transfer , author=. The Planetary Science Journal , volume=. 2022 , publisher=

    2022

  80. [80]

    IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing , volume=

    Emulation as an accurate alternative to interpolation in sampling radiative transfer codes , author=. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing , volume=. 2018 , publisher=

    2018

Showing first 80 references.