Rare Event Sampling Improves Mercury Instability Statistics

Abbot, Dorian S.; Webber, Robert J.; Hadden, Sam; Seligman, Darryl; Weare, Jonathan

doi:10.3847/1538-4357/ac2fa8

Title: Rare Event Sampling Improves Mercury Instability Statistics

Journal Article · 24 December 2021 · The Astrophysical Journal

DOI: https://doi.org/10.3847/1538-4357/ac2fa8 · OSTI ID:1981236

^[1];

^[2];

^[3]; Seligman, Darryl ^[4]; Weare, Jonathan ^[2]

Univ. of Chicago, IL (United States); Univ. of Chicago, IL (United States)
New York Univ. (NYU), NY (United States)
Harvard-Smithsonian Center for Astrophysics, Cambridge, MA (United States)
Univ. of Chicago, IL (United States)

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: New York Univ. (NYU), NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0020427

OSTI ID:: 1981236

Journal Information:: The Astrophysical Journal, Journal Name: The Astrophysical Journal Journal Issue: 2 Vol. 923; ISSN 0004-637X

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

References (49)

The evolution of habitable climates under the brightening Sun: THREE-DIMENSIONAL MODELING OF HOT CLIMATES Wolf, E. T.; Toon, O. B. Journal of Geophysical Research: Atmospheres, Vol. 120, Issue 12 https://doi.org/10.1002/2015JD023302	journal	June 2015
Minimum action method for the study of rare events E., Weinan; Ren, Weiqing; Vanden-Eijnden, Eric Communications on Pure and Applied Mathematics, Vol. 57, Issue 5 https://doi.org/10.1002/cpa.20005	journal	January 2004
Rare Event Simulation of Small Noise Diffusions Vanden-Eijnden, Eric; Weare, Jonathan Communications on Pure and Applied Mathematics, Vol. 65, Issue 12 https://doi.org/10.1002/cpa.21428	journal	September 2012
The design and analysis of a generalized RESTART/DPR algorithm for rare event simulation Dean, Thomas; Dupuis, Paul Annals of Operations Research, Vol. 189, Issue 1 https://doi.org/10.1007/s10479-009-0664-7	journal	November 2009
The chaotic motion of the solar system: A numerical estimate of the size of the chaotic zones Laskar, J. Icarus, Vol. 88, Issue 2 https://doi.org/10.1016/0019-1035(90)90084-M	journal	December 1990
Confirmation of resonant structure in the solar system Laskar, Jacques; Quinn, Thomas; Tremaine, Scott Icarus, Vol. 95, Issue 1 https://doi.org/10.1016/0019-1035(92)90196-E	journal	January 1992
Weighted-ensemble Brownian dynamics simulations for protein association reactions Huber, G. A.; Kim, S. Biophysical Journal, Vol. 70, Issue 1 https://doi.org/10.1016/S0006-3495(96)79552-8	journal	January 1996
The Torino Impact Hazard Scale Binzel, Richard P. Planetary and Space Science, Vol. 48, Issue 4 https://doi.org/10.1016/S0032-0633(00)00006-4	journal	April 2000
Chaotic diffusion in the Solar System Laskar, J. Icarus, Vol. 196, Issue 1 https://doi.org/10.1016/j.icarus.2008.02.017	journal	July 2008
Splitting for rare event simulation: A large deviation approach to design and analysis Dean, Thomas; Dupuis, Paul Stochastic Processes and their Applications, Vol. 119, Issue 2 https://doi.org/10.1016/j.spa.2008.02.017	journal	February 2009
Insulin Dissociates by Diverse Mechanisms of Coupled Unfolding and Unbinding Antoszewski, Adam; Feng, Chi-Jui; Vani, Bodhi P. The Journal of Physical Chemistry B, Vol. 124, Issue 27 https://doi.org/10.1021/acs.jpcb.0c03521	journal	June 2020
Maximizing Simulated Tropical Cyclone Intensity With Action Minimization Plotkin, David A.; Webber, Robert J.; O'Neill, Morgan E. Journal of Advances in Modeling Earth Systems, Vol. 11, Issue 4 https://doi.org/10.1029/2018MS001419	journal	April 2019
Rare Event Algorithm Study of Extreme Warm Summers and Heatwaves Over Europe Ragone, F.; Bouchet, F. Geophysical Research Letters, Vol. 48, Issue 12 https://doi.org/10.1029/2020GL091197	journal	June 2021
A numerical experiment on the chaotic behaviour of the Solar System Laskar, J. Nature, Vol. 338, Issue 6212 https://doi.org/10.1038/338237a0	journal	March 1989
Existence of collisional trajectories of Mercury, Mars and Venus with the Earth Laskar, J.; Gastineau, M. Nature, Vol. 459, Issue 7248 https://doi.org/10.1038/nature08096	journal	June 2009
REBOUND: an open-source multi-purpose N -body code for collisional dynamics Rein, H.; Liu, S. -F. Astronomy & Astrophysics, Vol. 537 https://doi.org/10.1051/0004-6361/201118085	journal	January 2012
A simple model of the chaotic eccentricity of Mercury Boué, G.; Laskar, J.; Farago, F. Astronomy & Astrophysics, Vol. 548 https://doi.org/10.1051/0004-6361/201219991	journal	November 2012
Long-term influence of asteroids on planet longitudes and chaotic dynamics of the solar system Woillez, E.; Bouchet, F. Astronomy & Astrophysics, Vol. 607 https://doi.org/10.1051/0004-6361/201731576	journal	November 2017
Long-term dynamics of the inner planets in the Solar System Mogavero, Federico; Laskar, Jacques Astronomy & Astrophysics, Vol. 655 https://doi.org/10.1051/0004-6361/202141007	journal	October 2021
Monte Carlo Methods for Estimating the Extreme Response of Dynamical Systems Naess, A.; Gaidai, O. Journal of Engineering Mechanics, Vol. 134, Issue 8 https://doi.org/10.1061/(ASCE)0733-9399(2008)134:8(628)	journal	August 2008
Monte Carlo Calculation of the Average Extension of Molecular Chains Rosenbluth, Marshall N.; Rosenbluth, Arianna W. The Journal of Chemical Physics, Vol. 23, Issue 2 https://doi.org/10.1063/1.1741967	journal	February 1955
Simulating rare events in equilibrium or nonequilibrium stochastic systems Allen, Rosalind J.; Frenkel, Daan; ten Wolde, Pieter Rein The Journal of Chemical Physics, Vol. 124, Issue 2 https://doi.org/10.1063/1.2140273	journal	January 2006
Umbrella sampling for nonequilibrium processes Warmflash, Aryeh; Bhimalapuram, Prabhakar; Dinner, Aaron R. The Journal of Chemical Physics, Vol. 127, Issue 15 https://doi.org/10.1063/1.2784118	journal	October 2007
Steered transition path sampling Guttenberg, Nicholas; Dinner, Aaron R.; Weare, Jonathan The Journal of Chemical Physics, Vol. 136, Issue 23 https://doi.org/10.1063/1.4724301	journal	June 2012
Practical rare event sampling for extreme mesoscale weather Webber, Robert J.; Plotkin, David A.; O’Neill, Morgan E. Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 29, Issue 5 https://doi.org/10.1063/1.5081461	journal	May 2019
Secular chaos and its application to Mercury, hot Jupiters, and the organization of planetary systems Lithwick, Yoram; Wu, Yanqin Proceedings of the National Academy of Sciences, Vol. 111, Issue 35 https://doi.org/10.1073/pnas.1308261110	journal	December 2013
Computation of extreme heat waves in climate models using a large deviation algorithm Ragone, Francesco; Wouters, Jeroen; Bouchet, Freddy Proceedings of the National Academy of Sciences, Vol. 115, Issue 1 https://doi.org/10.1073/pnas.1712645115	journal	December 2017
Adaptive Multilevel Splitting for Rare Event Analysis Cérou, Frédéric; Guyader, Arnaud Stochastic Analysis and Applications, Vol. 25, Issue 2 https://doi.org/10.1080/07362990601139628	journal	February 2007
Importance Sampling, Large Deviations, and Differential Games Dupuis, Paul; Wang, Hui Stochastics and Stochastic Reports, Vol. 76, Issue 6 https://doi.org/10.1080/10451120410001733845	journal	December 2004
Symplectic maps for the n-body problem Wisdom, Jack; Holman, Matthew The Astronomical Journal, Vol. 102 https://doi.org/10.1086/115978	journal	October 1991
Symplectic Correctors for Canonical Heliocentric n -Body Maps Wisdom, J. The Astronomical Journal, Vol. 131, Issue 4 https://doi.org/10.1086/500829	journal	April 2006
On the Dynamical Stability of the Solar System Batygin, Konstantin; Laughlin, Gregory The Astrophysical Journal, Vol. 683, Issue 2 https://doi.org/10.1086/589232	journal	August 2008
Resolving the Pericenter Wisdom, Jack The Astronomical Journal, Vol. 150, Issue 4 https://doi.org/10.1088/0004-6256/150/4/127	journal	September 2015
Theory of Secular Chaos and Mercury'S Orbit Lithwick, Yoram; Wu, Yanqin The Astrophysical Journal, Vol. 739, Issue 1 https://doi.org/10.1088/0004-637X/739/1/31	journal	September 2011
Dynamic Stability of the Solar System: Statistically Inconclusive Results from Ensemble Integrations Zeebe, Richard E. The Astrophysical Journal, Vol. 798, Issue 1 https://doi.org/10.1088/0004-637X/798/1/8	journal	December 2014
Chaotic Disintegration of the Inner Solar System Batygin, Konstantin; Morbidelli, Alessandro; Holman, Mathew J. The Astrophysical Journal, Vol. 799, Issue 2 https://doi.org/10.1088/0004-637X/799/2/120	journal	January 2015
Highly Stable Evolution of Earth'S Future Orbit Despite Chaotic Behavior of the Solar System Zeebe, Richard E. The Astrophysical Journal, Vol. 811, Issue 1 https://doi.org/10.1088/0004-637X/811/1/9	journal	September 2015
Unequal probability sampling without replacement through a splitting method Deville, J-C Biometrika, Vol. 85, Issue 1 https://doi.org/10.1093/biomet/85.1.89	journal	March 1998
High-order symplectic integrators for planetary dynamics and their implementation in rebound Rein, Hanno; Tamayo, Daniel; Brown, Garett Monthly Notices of the Royal Astronomical Society, Vol. 489, Issue 4 https://doi.org/10.1093/mnras/stz2503	journal	September 2019
REBOUNDx: a library for adding conservative and dissipative forces to otherwise symplectic N-body integrations Tamayo, Daniel; Rein, Hanno; Shi, Pengshuai Monthly Notices of the Royal Astronomical Society, Vol. 491, Issue 2 https://doi.org/10.1093/mnras/stz2870	journal	October 2019
Pruned-enriched Rosenbluth method: Simulations ofθpolymers of chain length up to 1 000 000 Grassberger, Peter Physical Review E, Vol. 56, Issue 3 https://doi.org/10.1103/PhysRevE.56.3682	journal	September 1997
Instantons for the Destabilization of the Inner Solar System Woillez, Eric; Bouchet, Freddy Physical Review Letters, Vol. 125, Issue 2 https://doi.org/10.1103/PhysRevLett.125.021101	journal	July 2020
Direct Evaluation of Large-Deviation Functions Giardinà, Cristian; Kurchan, Jorge; Peliti, Luca Physical Review Letters, Vol. 96, Issue 12 https://doi.org/10.1103/PhysRevLett.96.120603	journal	March 2006
Regression Shrinkage and Selection Via the Lasso Tibshirani, Robert Journal of the Royal Statistical Society: Series B (Methodological), Vol. 58, Issue 1 https://doi.org/10.1111/j.2517-6161.1996.tb02080.x	journal	January 1996
Chaotic Evolution of the Solar System Sussman, G. J.; Wisdom, J. Science, Vol. 257, Issue 5066 https://doi.org/10.1126/science.257.5066.56	journal	July 1992
The theory of direct probability redistribution and its application to rare event simulation Haraszti, Zsolt; Townsend, J. Keith ACM Transactions on Modeling and Computer Simulation, Vol. 9, Issue 2 https://doi.org/10.1145/333296.333349	journal	April 1999
Genealogical particle analysis of rare events Del Moral, Pierre; Garnier, Josselin The Annals of Applied Probability, Vol. 15, Issue 4 https://doi.org/10.1214/105051605000000566	journal	November 2005
Some Statistical Issues in Climate Science Stein, Michael L. Statistical Science, Vol. 35, Issue 1 https://doi.org/10.1214/19-STS730	journal	February 2020
A Repository of Vanilla Long-term Integrations of the Solar System Brown, Garett; Rein, Hanno Research Notes of the AAS, Vol. 4, Issue 12 https://doi.org/10.3847/2515-5172/abd103	journal	December 2020

Similar Records

Mercury’s Chaotic Secular Evolution as a Subdiffusive Process

Journal Article · 2024 · The Astrophysical Journal · OSTI ID:2580377

Abbot, Dorian; Webber, Robert; Hernandez, David; +2 more

THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT

Journal Article · 2011 · Astrophysical Journal · OSTI ID:21587517

Lithwick, Yoram; Yanqin, Wu

Highly stable evolution of Earth's future orbit despite chaotic behavior of the solar system

Journal Article · 2015 · Astrophysical Journal · OSTI ID:22882471

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
planetary dynamics

Title: Rare Event Sampling Improves Mercury Instability Statistics

Citation Formats

References (49)

Similar Records

Related Subjects