arxiv: 2604.16971 · v2 · submitted 2026-04-18 · 🌌 astro-ph.EP · astro-ph.IM

Recognition: no theorem link

Long-Term Dynamical Evolution and Ejection of Near-Earth Asteroids

(2) Inter-University Centre for Astronomy, Astrophysics (IUCAA), Badam Singh Kushvah (1), Chetan Abhijnanam Bora (1), Dhanbad, India, India), Kanak Saha (2) ((1) Indian Institute of Technology (ISM) Dhanbad, Pune

Authors on Pith no claims yet

Pith reviewed 2026-05-12 01:45 UTC · model grok-4.3

classification 🌌 astro-ph.EP astro-ph.IM

keywords Near-Earth asteroidsdynamical evolutionejectionmachine learningrecurrence plotschaotic motionnumerical integration

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The pith

Machine-learning models trained on initial elements or short recurrence plots can predict which near-Earth asteroids will be ejected from the Solar System.

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

The paper tests ensemble tree models on initial orbital elements and a convolutional neural network on recurrence plots from short MERCURY integrations as ways to classify long-term ejection outcomes without running expensive full simulations. These approaches achieve strong accuracy, with the trees performing well on ephemeris data and the network capturing chaotic temporal signatures at comparable or slightly better levels. Forward and backward integrations show only partial overlap in ejected sets, revealing time-asymmetric behavior in chaotic regions. Stable asteroids map to known dynamical groups, confirming the role of starting configuration. The methods supply scalable complements to numerical work for prioritizing detailed studies and planetary-defense planning.

Core claim

Ensemble tree classifiers on initial orbital elements and a convolutional neural network on recurrence plots from brief integrations classify long-term ejection of near-Earth asteroids at accuracy comparable to or exceeding full high-accuracy simulations, while backward runs expose time-asymmetric ejection and stable objects align with established dynamical families.

What carries the argument

Recurrence plots generated from short-period MERCURY integrations, fed to a convolutional neural network to extract temporal signatures of chaotic motion, alongside ensemble tree models trained directly on ephemeris inputs.

If this is right

Non-ejected asteroids correspond to known dynamical groups, showing initial configuration strongly constrains long-term stability.
Partial overlap between forward- and reverse-ejected sets indicates time-asymmetric behavior that full simulations must account for.
The methods allow rapid screening to prioritize asteroids needing detailed numerical study.
Scalable classification supports planetary-defense analyses by quickly identifying potential ejection or impact risks.

Where Pith is reading between the lines

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

The same short-integration-plus-recurrence-plot pipeline could be tested on other small-body populations exhibiting chaos, such as centaurs or trans-Neptunian objects.
If the models generalize, they might reduce the computational cost of mapping stability boundaries in resonant regions by orders of magnitude.
Combining the tree and CNN outputs could yield an ensemble that flags cases where short-term data are insufficient, prompting targeted long integrations.

Load-bearing premise

Short integrations produce recurrence plots whose patterns suffice to forecast long-term ejection without overlooking rare chaotic transitions that only appear over much longer times.

What would settle it

Run full long-term integrations on a test set of asteroids and measure whether the model's ejection predictions match the actual outcomes at the reported accuracy level.

Figures

Figures reproduced from arXiv: 2604.16971 by (2) Inter-University Centre for Astronomy, Astrophysics (IUCAA), Badam Singh Kushvah (1), Chetan Abhijnanam Bora (1), Dhanbad, India, India), Kanak Saha (2) ((1) Indian Institute of Technology (ISM) Dhanbad, Pune.

**Figure 1.** Figure 1: Distribution of ejected and non-ejected asteroids in terms of their semi-major axis and eccentricity, with inclination values represented by the colour scale. The marginal histograms on the top and right illustrate the normalized distributions of the semi-major axis and eccentricity for both classes, while the top-right inset shows the inclination distribution. stronger resonant interactions and enhanced c… view at source ↗

**Figure 2.** Figure 2: Comparative orbital evolution and recurrence structure of asteroids 2007 VP243 and 2005 WE55 over a 0.2 Myr interval. (a) Semi-major axis and eccentricity evolution of the dynamically unstable asteroid 2007 VP243, showing large semi-major axis excursions and irregular eccentricity growth indicative of chaotic diffusion. (b) RP of 2007 VP243, exhibiting fragmented, non-periodic structures characteristic of … view at source ↗

**Figure 3.** Figure 3: Traditional ML models and CNN-based pipeline. A comparative analysis between these ML models and the proposed DL models is performed to evaluate improvements in predictive performance. 5.1. Machine Learning Models The ML models selected for this study are chosen based on their proven effectiveness in structured data classification tasks (W. Wang et al. 2020). They are recognized for their capacity to manag… view at source ↗

**Figure 4.** Figure 4: CNN architecture used for classification of RPs. Model Key hyperparameters tuned KNN n_neighbors, weights Decision Tree max_depth, min_samples_split RF/ExtraTree n_estimators, max_features AdaBoost/GB n_estimators, learning_rate MLP hidden_layer_sizes, alpha (L2) [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗

**Figure 5.** Figure 5: Confusion matrices for seven classification models shown in a unified 2×2 layout separating true positives (TP), false negatives (FN), false positives (FP), and true negatives (TN). Coloured bars denote individual models, ordered by decreasing overall performance from left to right, with bar heights normalized by the total number of objects in the corresponding true class. Numerical annotations indicate ab… view at source ↗

**Figure 6.** Figure 6: Model performance summary. (a) Training and validation loss as a function of epoch, illustrating rapid initial convergence followed by gradual stabilization. (b) Training and validation accuracy across epochs, showing consistent improvement and convergence between the two sets. (c) PR curve on the test set, characterizing the trade-off between precision and recall; the shaded region represents the area un… view at source ↗

**Figure 7.** Figure 7: Confusion Matrix for CNN Model. To further evaluate generalization, classification metrics were assessed on the test set. The model achieved a test loss of 0.3874 and a test accuracy of 0.8689. Although slightly lower than the validation results, this minor decrease is expected, as the test set may contain more complex or ambiguous instances not fully represented in the training data (R. Roelofs 2019; J. B… view at source ↗

**Figure 8.** Figure 8: Number of asteroid ejections per 100,000-year interval over a one-million-year timespan. by a dashed blue line, reveal a distinct temporal trend in ejection rates. The statistics shown here are derived from the complete integrated dataset, including both real and synthetically generated NEAs, comprising approximately 70,000 integration cases. During the early phase (0.1-0.3 Myr), the number of ejections ri… view at source ↗

**Figure 9.** Figure 9: Distribution of semi-major axis versus eccentricity for ejected and non-ejected asteroids across different NEA subgroups. The clustering of ejected asteroids within this restricted orbital range underscores the significance of initial orbital conditions and dynamical interactions in determining the long-term stability of NEAs. 6.4.3. Backward Integration and Dynamical Behaviour of Ejected Asteroids To expl… view at source ↗

**Figure 10.** Figure 10: Time evolution of orbital eccentricity for different ejection outcomes in forward and backward integrations. (a) Ejection (forward): asteroids ejected in the forward integration but remaining bound in the backward integration. (b) Ejection (forward and backward): asteroids ejected in both integration directions. (c) No ejection: asteroids that remain bound in both forward and backward integrations. (d) Ej… view at source ↗

read the original abstract

Long-term integrations of asteroid orbits with high-accuracy numerical integrators are essential for understanding dynamical evolution and ejection from the Solar System, but are computationally expensive. Here, we investigate the dynamical behaviour of asteroids and explore machine-learning (ML) and deep-learning (DL) approaches as efficient, scalable alternatives for classifying long-term dynamical outcomes. While the ML classifiers are trained on initial orbital elements, the convolutional neural network is trained on recurrence plots derived from short-period numerical integrations generated with the MERCURY integrator. Ensemble tree models perform strongly on the ephemeris input, and the neural network captures temporal signatures of chaotic motion with comparable or slightly improved accuracy. Backward integrations reveal partial overlap between forward- and reverse-ejected sets, illustrating time-asymmetric behaviour in chaotic regions; these backward results are interpreted only as diagnostic probes rather than reconstructions of past histories. Non-ejected asteroids largely correspond to known dynamical groups, underscoring the constraining role of initial orbital configuration. These methods provide scalable frameworks to complement numerical integrations and inform prioritisation for detailed long-term dynamical studies, with implications for planetary-defence analyses.

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.

Desk Editor's Note private letter to a colleague

ML on short integrations for asteroid ejection classification is a reasonable efficiency idea but the abstract gives no numbers or validation to judge if it actually works.

read the letter

This paper tries to replace expensive long-term numerical integrations of near-Earth asteroid orbits with machine learning classifiers. Ensemble trees work on initial orbital elements, while a CNN is trained on recurrence plots made from short MERCURY runs to predict ejection outcomes. They also check backward integrations for time asymmetry and note that stable objects fall into known dynamical groups. The approach aims at scalable screening for planetary defense work.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes machine-learning classifiers (ensemble trees) trained on initial orbital elements and a convolutional neural network trained on recurrence plots generated from short-period MERCURY integrations as scalable alternatives to expensive long-term numerical integrations for classifying ejection outcomes of near-Earth asteroids. It reports that the tree models perform strongly on ephemeris input while the CNN captures temporal signatures of chaotic motion with comparable or slightly improved accuracy, notes partial overlap between forward- and backward-ejected sets, and concludes that non-ejected asteroids align with known dynamical groups.

Significance. If the performance claims are substantiated with quantitative validation against long-term integrations, the approach could offer a useful complement to direct N-body runs for prioritizing targets in planetary-defense studies and dynamical surveys. The recurrence-plot CNN is a potentially interesting way to encode short-term chaotic signatures, and the forward/backward asymmetry observation is a useful diagnostic reminder of time-irreversibility in chaotic regions.

major comments (3)

[Abstract and §3] Abstract and §3 (training description): the claims that ensemble trees 'perform strongly' and the CNN achieves 'comparable or slightly improved accuracy' are presented without any numerical metrics, confusion matrices, ROC-AUC values, training-set sizes, or cross-validation details. Because the central claim is that these methods are efficient, scalable alternatives, the absence of these quantities makes the performance assertion impossible to evaluate.
[§2.2 and §4] §2.2 and §4 (recurrence-plot construction and CNN results): no ablation on integration length, no direct comparison of CNN predictions against full long-term MERCURY runs for the same objects, and no discussion of how rare resonance crossings or close encounters occurring after the short integration window are captured. This leaves the weakest assumption—that short-window recurrence plots contain all outcome-determining chaotic features—untested and load-bearing for the generalization claim.
[§5] §5 (backward-integration analysis): the partial overlap between forward- and reverse-ejected sets is reported, yet no quantitative measure (e.g., Jaccard index or contingency table) is supplied, nor is a control experiment shown that would demonstrate the overlap is not simply an artifact of the short integration length used for both directions.

minor comments (2)

[§2.2] Notation for the recurrence-plot parameters (embedding dimension, delay, threshold) is introduced without a dedicated table or explicit listing of the values adopted for the full dataset.
[Figures 2 and 4] Figure captions for the recurrence-plot examples and the CNN architecture diagram should explicitly state the integration length and number of asteroids represented.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review. The comments identify important areas for improving the transparency and robustness of our claims. We address each major comment point by point below and describe the revisions we will implement.

read point-by-point responses

Referee: [Abstract and §3] Abstract and §3 (training description): the claims that ensemble trees 'perform strongly' and the CNN achieves 'comparable or slightly improved accuracy' are presented without any numerical metrics, confusion matrices, ROC-AUC values, training-set sizes, or cross-validation details. Because the central claim is that these methods are efficient, scalable alternatives, the absence of these quantities makes the performance assertion impossible to evaluate.

Authors: We agree that the absence of explicit quantitative metrics in the abstract and training description hinders evaluation of the central performance claims. We will revise the abstract to include key numerical results (overall accuracies, AUC scores, and a brief note on training-set size and cross-validation). In §3 we will add a dedicated summary table or subsection that reports training-set sizes, the cross-validation procedure, confusion matrices, and ROC-AUC values for both the ensemble-tree and CNN models. These changes will make the performance assertions directly verifiable. revision: yes
Referee: [§2.2 and §4] §2.2 and §4 (recurrence-plot construction and CNN results): no ablation on integration length, no direct comparison of CNN predictions against full long-term MERCURY runs for the same objects, and no discussion of how rare resonance crossings or close encounters occurring after the short integration window are captured. This leaves the weakest assumption—that short-window recurrence plots contain all outcome-determining chaotic features—untested and load-bearing for the generalization claim.

Authors: We acknowledge that an explicit ablation on integration length and a clearer statement of the validation procedure are needed to test the core assumption. We will add an ablation study in §4 that varies the short-integration length used to generate recurrence plots and reports the resulting change in CNN accuracy. We will also clarify that the CNN was trained and evaluated on a held-out test set for which independent long-term MERCURY integrations provided the ground-truth labels, and we will expand the discussion to address the possibility that rare late resonance crossings or encounters may not be captured, including the implications for generalization. revision: yes
Referee: [§5] §5 (backward-integration analysis): the partial overlap between forward- and reverse-ejected sets is reported, yet no quantitative measure (e.g., Jaccard index or contingency table) is supplied, nor is a control experiment shown that would demonstrate the overlap is not simply an artifact of the short integration length used for both directions.

Authors: We agree that quantitative measures and a control experiment would strengthen the backward-integration analysis. In the revised §5 we will report the Jaccard index together with a contingency table that quantifies the overlap between the forward- and backward-ejected sets. We will also add a control experiment that repeats the backward integrations with a longer short-integration window and compares the resulting overlap; this will test whether the observed partial overlap is robust or sensitive to integration length. revision: yes

Circularity Check

0 steps flagged

No significant circularity in ML/DL prediction of long-term asteroid outcomes

full rationale

The paper trains standard ensemble classifiers on initial orbital elements and a CNN on recurrence plots generated from short MERCURY integrations, using these features to predict labels for long-term ejection outcomes obtained from separate long-term simulations. This is a conventional supervised learning setup in which the target variable (long-term dynamical fate) is independent of the input features by construction; no equation, ansatz, or self-citation reduces the reported accuracy or classification performance to a tautology or to the fitted parameters themselves. No uniqueness theorems, self-referential definitions, or renaming of known results appear in the provided abstract or description. The work is therefore self-contained as an empirical approximation task rather than a closed derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that short-term chaotic signatures are predictive of long-term ejection without additional free parameters beyond standard integrator settings and ML hyperparameters.

axioms (1)

domain assumption Short-period numerical integrations capture sufficient temporal signatures of chaotic motion to classify long-term ejection outcomes.
Invoked when training the CNN on recurrence plots from short integrations to stand in for full long-term runs.

pith-pipeline@v0.9.0 · 5542 in / 1247 out tokens · 33666 ms · 2026-05-12T01:45:58.618375+00:00 · methodology

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