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arxiv: 2605.22862 · v1 · pith:DIUPGMS2new · submitted 2026-05-19 · 🌀 gr-qc · hep-th

Constraining Black Hole Parameters in Non-Commutative Geometry using Machine Learning

Maryem Jemri This is my paper

Pith reviewed 2026-05-25 05:53 UTC · model grok-4.3

classification 🌀 gr-qc hep-th
keywords non-commutative geometryblack hole shadowsmachine learningEvent Horizon TelescopeSgr A*string cloudsdark energyCUDA computations
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The pith

Machine learning on black hole shadows shows non-commutative geometry model fits Sgr A* Keck data.

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

The paper applies machine learning combined with CUDA computations to constrain parameters of non-commutative black holes that include string clouds and dark energy sectors. It first calculates the event horizon structure and then numerically determines shadow properties and energy emission rates for rotating and charged cases. A fully connected neural network is trained on the resulting datasets to classify which parameter combinations match Event Horizon Telescope observations. The central finding is that the model remains consistent with Sgr A* Keck black hole data. A sympathetic reader would care because the work supplies a concrete computational route for testing string-theory-motivated geometries against real astronomical measurements.

Core claim

By generating numerical shadow and emission data via CUDA for non-commutative rotating and charged black holes with string clouds and dark energy, then training a fully connected neural network on those data, the authors establish that the non-commutative model under study produces parameter sets consistent with the observational data provided by Event Horizon Telescope collaborations for Sgr A* Keck black holes.

What carries the argument

Fully connected neural network trained on CUDA-generated numerical datasets of black hole shadows and energy emission rates to classify parameter consistency with EHT observations.

Load-bearing premise

The CUDA numerical calculations of shadows and emissions accurately represent the observable properties of the non-commutative black holes, and the neural network can reliably identify which parameter sets match the real data.

What would settle it

Observing a shadow size or shape for Sgr A* that lies outside the range produced by any parameter set in the non-commutative model would show the claimed consistency does not hold.

Figures

Figures reproduced from arXiv: 2605.22862 by Maryem Jemri.

Figure 1
Figure 1. Figure 1: Regions in the (a, b) plane where the metric admits at least one real event horizon radius. 3 NC black hole shadows and energy emission rate using CUDA computations In this section, we investigate certain optical properties of rotating and charged NC black holes with a cloud of strings and quintessence in NC geometry by applying CUDA techniques. Precisely, we analyze the effect the involved parameters on b… view at source ↗
Figure 2
Figure 2. Figure 2: Effect of internal parameters on the shadow behavior. size extends up to values of approximately 45, unlike ordinary charged black holes, where the radius generally does not exceed 25. This difference can be attributed to the additional terms in the metric, in which the parameter b couples with the charge Q. Then, the effect of the string cloud parameter α and the quintessence parameter N are examined by v… view at source ↗
Figure 3
Figure 3. Figure 3: Effect of α (left panel) and N (right panel) on the black hole shadow behavior. As illustrated in Fig. (3), the shadow exhibits a D-like deformation in the regime of large N and small α. This characteristic gradually reduces as α increases or N decreases, which indicates that these two parameters have a similar influence on the distortion of the shadow curves. We now examine the effect of the NC parameter … view at source ↗
Figure 4
Figure 4. Figure 4: Effect of the parameter b on the shadow behavior. in Fig. (4), such a parameter controls both the size and the global shape of the shadow. Increasing b leads to a larger and more extended shadows, whereas smaller values of b yield a more compact and nearly circular geometric configurations. In contrast, the parameters N and α have less effects, mainly changing the shape of the shadow boundary rather than i… view at source ↗
Figure 5
Figure 5. Figure 5: Variation of the energy emission rate as a function of the emission frequency for different values of a and Q [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Variation of the energy emission rate as a function of the emission frequency for different values of η. these results clearly show the attenuating effect of these two parameters on the emission spectrum. From the four panels in Fig. (7), we analyze the effect of the NC parameter b on the energy emission rate for different values of N and α. In all cases, the general behavior follows a similar behavior. In… view at source ↗
Figure 7
Figure 7. Figure 7: Variation of the energy emission rate as a function of the emission frequency for different values of b . 4 Constraints on NC rotating black hole parameters from EHT observations using CUDA techniques In order to establish a bridge between the theoretical predictions and the observational data, this section provides an analysis of the shadow cast by rotating NC quintessence Reissner–Nordstr¨om black holes … view at source ↗
Figure 8
Figure 8. Figure 8: Combined constraint regions in the parameter spaces (α, b), (Q, b),(a, b), and (N, b) obtained from CUDA-based simulations. 5 Machine learning constraints on NC black hole pa￾rameters from EHT observations In this section, we would like to apply machine learning techniques to the shadow activities. This approach has been motivated by recent developments in the application of machine learning to the physics… view at source ↗
Figure 9
Figure 9. Figure 9: Voting procedure for consistency of the shadow with EHT observations [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Training curves of the FCNN model for the 1 [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Training curves of the FCNN model for the 2 [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
read the original abstract

Motivated by string theory, we constrain non-commutative black hole parameters through shadow behaviors using machine learning techniques combined by CUDA computations. To do so, we first investigate the structure of the event horizon of non-commutative black holes in the presence of string clouds and dark energy sectors by exploiting CUDA-based methods. We numerically approach the shadow properties and the energy emission rate of rotating and charged black holes in non-commutative geometry via such high-performance parallel computings. To bridge these findings with observational data, we implement a CUDA-based framework in order to constrain the involved black hole parameters including the non-commutative one. Using the resulting numerical data, we build a robust training datasets for a fully connected neural network to determine whether a given set of parameters matches with the observational data provided by Event Horizon Telescope collaborations. As a result, we find that the non-commutative model under study is consistent with the observations of $SgrA^*_{\mathrm{Keck}}$ black holes.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 1 minor

Summary. The manuscript uses CUDA-based numerical methods to compute event horizons, shadows, and energy emission rates for rotating and charged non-commutative black holes in the presence of string clouds and dark energy. It then generates training data from these calculations to train a fully connected neural network that constrains the black hole parameters (including the non-commutative parameter) by matching to EHT observational data, ultimately concluding that the non-commutative model is consistent with Sgr A* Keck observations.

Significance. If the neural network training and validation were shown to be robust, the combination of high-performance parallel computing with machine learning could provide an efficient framework for exploring and constraining parameter spaces in modified gravity models against shadow observations. The approach has potential methodological value for future studies of exotic black hole solutions, but the current lack of reported performance metrics substantially reduces its immediate impact.

major comments (1)
  1. [Neural network training description] The description of the neural network (abstract and methods) provides no architecture details, loss function, training/validation split, accuracy on held-out data, or confusion matrix. Since the central claim of consistency with SgrA* Keck data rests on the network correctly identifying matching parameter sets from the CUDA-generated synthetic data, the absence of these metrics makes it impossible to assess generalization versus overfitting, directly undermining the reliability of the reported result.
minor comments (1)
  1. [Abstract] The abstract refers to 'robust training datasets' without specifying the parameter ranges sampled or the precise EHT observables (e.g., shadow diameter, asymmetry) used for matching.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed review and constructive criticism. The major comment highlights a genuine gap in the current manuscript regarding the neural network implementation details, which we address directly below by committing to a substantial revision of the methods section.

read point-by-point responses

  1. Referee: [Neural network training description] The description of the neural network (abstract and methods) provides no architecture details, loss function, training/validation split, accuracy on held-out data, or confusion matrix. Since the central claim of consistency with SgrA* Keck data rests on the network correctly identifying matching parameter sets from the CUDA-generated synthetic data, the absence of these metrics makes it impossible to assess generalization versus overfitting, directly undermining the reliability of the reported result.

    Authors: We agree that the absence of these specifics prevents a proper evaluation of the neural network's reliability and generalization. The current manuscript indeed provides only a high-level statement that a fully connected neural network was trained on the CUDA-generated datasets without further elaboration. In the revised version we will add a dedicated subsection in the methods that specifies: (i) the architecture (number of hidden layers, neurons per layer, activation functions), (ii) the loss function and optimizer, (iii) the train/validation/test split ratios together with the rationale, (iv) quantitative performance metrics on held-out data (accuracy, loss curves), and (v) a confusion matrix or equivalent diagnostic for the classification task of matching parameter sets to observations. These additions will directly address concerns about overfitting and will strengthen the evidential basis for the consistency claim with Sgr A* Keck data. revision: yes

Circularity Check

1 steps flagged

Consistency with EHT data is output of NN classifier trained on match labels derived from the same data

specific steps
  1. fitted input called prediction [Abstract]
    "Using the resulting numerical data, we build a robust training datasets for a fully connected neural network to determine whether a given set of parameters matches with the observational data provided by Event Horizon Telescope collaborations. As a result, we find that the non-commutative model under study is consistent with the observations of $SgrA^*_{Keck}$ black holes."

    Training labels are assigned by comparing the model's own CUDA-computed shadows to EHT data; the NN learns this match criterion and the reported consistency is the NN's classification output on the target parameter set. The result is therefore statistically forced by the construction of the training labels rather than an out-of-sample prediction.

full rationale

The paper generates synthetic shadow data for non-commutative black hole parameters, labels parameter sets as matching EHT observations by direct comparison, trains an NN on those labels, and then reports that the model is consistent because the NN identifies matching parameters. This makes the central consistency claim a direct product of the fitting/classification procedure rather than an independent verification. No other circular patterns (self-citation chains, self-definitional equations, or imported uniqueness theorems) appear in the provided text.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger records only the elements explicitly named there.

free parameters (1)
  • non-commutative parameter
    The central parameter being constrained by the neural network against EHT data.
axioms (1)
  • domain assumption Non-commutative geometry motivated by string theory
    Stated motivation for the model in the abstract.

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Reference graph

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