Long Time Propagation of Stochasticity by Dynamical Polynomial Chaos Expansions

Ozen, H. Cagan

doi:10.7916/d8wh32c5

Cited by 2 publications

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“…Here, we will focus on a rather large and popular class of these methods that uses polynomial expansions to model the dependency of the state variables or, directly, the quantity of interest, on the uncertain quantities. Among them, it is worth mentioning methods that propagate highorder Taylor polynomials (Massari et al 2017;Pérez-Palau et al 2015), polynomial chaos expansions (PCE) (Bhusal and Subbarao 2019;Ozen 2017;Gerritsma et al 2010;Schick and Heuveline 2014) and Chebyshev polynomials (Vasile et al 2019).…”

Section: Introductionmentioning

confidence: 99%

Polynomial stochastic dynamical indicators

Vasile

Manzi

2023

Celest Mech Dyn Astron

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This paper introduces three types of dynamical indicators that capture the effect of uncertainty on the time evolution of dynamical systems. Two indicators are derived from the definition of finite-time Lyapunov exponents, while a third indicator directly exploits the property of the polynomial expansion of the dynamics with respect to the uncertain quantities. The paper presents the derivation of the indicators and a number of numerical experiments that illustrates the use of these indicators to depict a cartography of the phase space under parametric uncertainty and to identify robust initial conditions and regions of practical stability in the restricted three-body problem.

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Section: Introductionmentioning

confidence: 99%

Polynomial stochastic dynamical indicators

Vasile

Manzi

2023

Celest Mech Dyn Astron

View full text Add to dashboard Cite

show abstract

“…Here we will focus on a rather large and popular class of these methods that uses polynomial expansions to model the dependency of the state variables or, directly, the quantity of interest, on the uncertain quantities. Among them it is worth mentioning methods that propagate high-order Taylor polynomials [2,3], Polynomial Chaos Expansions (PCE) [4][5][6][7] and Chebyshev polynomials [8].…”

Section: Introductionmentioning

confidence: 99%

Polynomial Stochastic Dynamical Indicators

Vasile

Manzi

2022

Preprint

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This paper introduces three types of dynamical indicators that capturethe effect of uncertainty on the time evolution of dynamical systems. Two indica-tors are derived from the definition of Finite Time Lyapunov Exponents while athird indicator directly exploits the property of the polynomial expansion of thedynamics with respect to the uncertain quantities. The paper presents the deriva-tion of the indicators and a number of numerical experiments that illustrates theuse of these indicators to depict a cartography of the phase space under paramet-ric uncertainty and to identify robust initial conditions and regions of practicalstability in the restricted three-body problem.

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Long Time Propagation of Stochasticity by Dynamical Polynomial Chaos Expansions

Cited by 2 publications

References 0 publications

Polynomial stochastic dynamical indicators

Polynomial stochastic dynamical indicators

Polynomial Stochastic Dynamical Indicators

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