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Rare Event Sampling Improves Mercury Instability Statistics
Earth and Planetary Astrophysics · Submitted 16 Jun 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In this paper we use a new rare event sampling technique, Quantile Diffusion Monte Carlo (QDMC), to estimate that the probability of a Mercury instability event in the next 2 billion years is approximately $10^{-4}$ in the REBOUND N-body code.
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The abstract, sentence by sentence
Due to the chaotic nature of planetary dynamics, there is a non-zero probability that Mercury's orbit will become unstable in the future. Previous efforts have estimated the probability of this happening between 3 and 5 billion years in the future using a large number of direct numerical simulations with an N-body code, but were not able to obtain accurate estimates before 3 billion years in the future because Mercury instability events are too rare. In this paper we use a new rare event sampling technique, Quantile Diffusion Monte Carlo (QDMC), to estimate that the probability of a Mercury instability event in the next 2 billion years is approximately $10^{-4}$ in the REBOUND N-body code. We show that QDMC provides unbiased probability estimates at a computational cost of up to 100 times less than direct numerical simulation. QDMC is easy to implement and could be applied to many problems in planetary dynamics in which it is necessary to estimate the probability of a rare event.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Due to the chaotic nature of planetary dynamics, there is a non-zero probability that Mercury's orbit will become unstable in the future. | background 1.00 | 0.07 | 0.02 | asserted 0.53 |
| s1 | Previous efforts have estimated the probability of this happening between 3 and 5 billion years in the future using a large number of direct numerical simulations with an N-body code, but were not able to obtain accurate estimates before 3 billion years in the future because Mercury instability events are too rare. | gap 0.82 | 0.04 | 0.03 | asserted 1.00 |
| s2 | In this paper we use a new rare event sampling technique, Quantile Diffusion Monte Carlo (QDMC), to estimate that the probability of a Mercury instability event in the next 2 billion years is approximately $10^{-4}$ in the REBOUND N-body code. | result 0.88 | 0.97 | 0.85 | asserted 0.97 |
| s3 | We show that QDMC provides unbiased probability estimates at a computational cost of up to 100 times less than direct numerical simulation. | result 0.97 | 0.96 | 0.21 | asserted 1.00 |
| s4 | QDMC is easy to implement and could be applied to many problems in planetary dynamics in which it is necessary to estimate the probability of a rare event. | interpretation 0.52 | 0.55 | 0.08 | hedged possibility 0.84 |
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The paper
Original abstract
Due to the chaotic nature of planetary dynamics, there is a non-zero probability that Mercury's orbit will become unstable in the future. Previous efforts have estimated the probability of this happening between 3 and 5 billion years in the future using a large number of direct numerical simulations with an N-body code, but were not able to obtain accurate estimates before 3 billion years in the future because Mercury instability events are too rare. In this paper we use a new rare event sampling technique, Quantile Diffusion Monte Carlo (QDMC), to estimate that the probability of a Mercury instability event in the next 2 billion years is approximately $10^{-4}$ in the REBOUND N-body code. We show that QDMC provides unbiased probability estimates at a computational cost of up to 100 times less than direct numerical simulation. QDMC is easy to implement and could be applied to many problems in planetary dynamics in which it is necessary to estimate the probability of a rare event.
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References
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3 arXiv papers cite this in 8 sentences
Papers citing it · 5 sentences without a confident label
Compares with it 1 paper
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We find significant differences in the evolution of Mercury's eccentricity between the data sets of [ref] and [ref] , and we postulate this is due to different levels of pericenter resolution.
Stepsize errors in the $N$-body problem: discerning Mercury's true possible long-term orbits · Discussion · 0.90
Cites it as support 1 paper
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We can find some supporting evidence for this already from [ref] , Figure 3.
Stepsize errors in the $N$-body problem: discerning Mercury's true possible long-term orbits · Solar System integrations in the literature · 0.96
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