Rare Event Sampling Improves Mercury Instability Statistics
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...
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| Vydáno v: | The Astrophysical journal Ročník 923; číslo 2; s. 236 - 244 |
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The American Astronomical Society
01.12.2021
IOP Publishing |
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| ISSN: | 0004-637X, 1538-4357 |
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| 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. |
|---|---|
| AbstractList | 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. 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. 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. |
| Author | Hadden, Sam Weare, Jonathan Abbot, Dorian S. Seligman, Darryl Webber, Robert J. |
| Author_xml | – sequence: 1 givenname: Dorian S. orcidid: 0000-0001-8335-6560 surname: Abbot fullname: Abbot, Dorian S. organization: Department of the Geophysical Sciences, The University of Chicago, Chicago , IL 60637 ; USA – sequence: 2 givenname: Robert J. orcidid: 0000-0001-8286-6315 surname: Webber fullname: Webber, Robert J. organization: Courant Institute of Mathematical Sciences, New York University, New York , NY 10012 USA – sequence: 3 givenname: Sam orcidid: 0000-0002-1032-0783 surname: Hadden fullname: Hadden, Sam organization: Harvard-Smithsonian Center for Astrophysics, The Institute for Theory and Computation, Cambridge, MA 02138, USA – sequence: 4 givenname: Darryl surname: Seligman fullname: Seligman, Darryl organization: Department of the Geophysical Sciences, The University of Chicago, Chicago , IL 60637 ; USA – sequence: 5 givenname: Jonathan surname: Weare fullname: Weare, Jonathan organization: Courant Institute of Mathematical Sciences, New York University, New York , NY 10012 USA |
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| Snippet | 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... 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... |
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| SubjectTerms | ASTRONOMY AND ASTROPHYSICS Astrophysics Computer simulation Direct numerical simulation Dynamic stability Estimates Instability Mercury Mercury (planet) Numerical simulations Orbital mechanics Planetary dynamics Sampling methods Sampling techniques |
| Title | Rare Event Sampling Improves Mercury Instability Statistics |
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