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Universal upper estimate for prediction errors under moderate model uncertainty.

Bálint Kaszás1, George Haller1

  • 1Institute for Mechanical Systems, ETH Zürich, Leonhardstrasse 21, 8092 Zürich, Switzerland.

Chaos (Woodbury, N.Y.)
|December 2, 2020
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Summary
This summary is machine-generated.

We developed optimal upper bounds for model prediction error, even with unknown model uncertainty. These bounds, based on strain tensor invariants, quantify trajectory uncertainty using model sensitivity (MS).

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Area of Science:

  • * Mechanics and Dynamical Systems
  • * Applied Mathematics
  • * Uncertainty Quantification

Background:

  • * Model prediction error is a critical concern in scientific and engineering applications.
  • * Quantifying uncertainty in complex systems often relies on assumptions about model accuracy.
  • * Existing methods may not adequately address unknown or moderate model uncertainties.

Purpose of the Study:

  • * To derive universal upper estimates for model prediction error under unknown model uncertainty.
  • * To establish optimal bounds on trajectory uncertainty based on system invariants.
  • * To introduce and validate model sensitivity (MS) as a key metric for assessing uncertainty impacts.

Main Methods:

  • * Derivation of universal upper bounds for prediction error using invariants of the Cauchy-Green strain tensor.
  • * Analysis of trajectory uncertainty as a function of model invariants.
  • * Introduction of model sensitivity (MS) as a measure relating trajectory uncertainty to model uncertainty.

Main Results:

  • * Developed optimal, universal upper estimates for model prediction error under unknown model uncertainty.
  • * Demonstrated that trajectory uncertainty bounds are solely functions of strain tensor invariants.
  • * Identified model sensitivity (MS) as a crucial tool for assessing the global impact of modeling uncertainties across phase space.

Conclusions:

  • * The derived bounds are optimal and cannot be improved for general systems.
  • * Model sensitivity (MS) provides a valuable and efficient method for evaluating the influence of modeling uncertainties.
  • * Finite-time Lyapunov exponents do not generally capture sensitivity to modeling errors, but MS retains key features.