Uncertainty quantification by using Lie theory

Marc Jornet

Chaos, Solitons & Fractals, 2022, vol. 155, issue C

Abstract: In this short communication, the application of Lie theory in the context of forward uncertainty quantification for random ordinary differential equations is investigated. Two topics are treated. The first one concerns the automation of the Taylor series solution to an autonomous random ordinary differential equation through the Lie transformation, to derive its statistics by linearity. The second topic is about random Hamiltonian systems; when polynomial expansions of the solution are considered, the Lie formalism allows for constructing high order integrators for the Galerkin system of the expansion coefficients. These ideas are developed theoretically and assessed numerically.

Keywords: Uncertainty propagation; Differential equation with uncertain parameters; Lie methods; Taylor series; Galerkin system (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010936

DOI: 10.1016/j.chaos.2021.111739

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