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• W2945447780 abstract "We develop a systematic information-theoretic framework for quantification and mitigation of error in probabilistic Lagrangian (i.e., path-based) predictions which are obtained from dynamical systems generated by uncertain (Eulerian) vector fields. This work is motivated by the desire to improve Lagrangian predictions in complex dynamical systems based either on analytically simplified or data-driven models. We derive a hierarchy of general information bounds on uncertainty in estimates of statistical observables $mathbb{E}^{nu}[f]$, evaluated on trajectories of the approximating dynamical system, relative to the true'' observables $mathbb{E}^{mu}[f]$ in terms of certain $varphi$-divergences, $mathcal{D}_varphi(mu|nu)$, which quantify discrepancies between probability measures $mu$ associated with the original dynamics and their approximations $nu$. We then derive two distinct bounds on $mathcal{D}_varphi(mu|nu)$ itself in terms of the Eulerian fields. This new framework provides a rigorous way for quantifying and mitigating uncertainty in Lagrangian predictions due to Eulerian model error." @default.
• W2945447780 created "2019-05-29" @default.
• W2945447780 creator A5056194720 @default.
• W2945447780 creator A5080219858 @default.
• W2945447780 date "2019-05-21" @default.
• W2945447780 modified "2023-09-28" @default.
• W2945447780 title "Lagrangian uncertainty quantification and information inequalities for stochastic flows" @default.
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• W2945447780 doi "https://doi.org/10.48550/arxiv.1905.08707" @default.
• W2945447780 hasPublicationYear "2019" @default.
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