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2018

Mori-Zwanzig reduced models for uncertainty quantification

Li, Jing, Stinis, Panos

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In many time-dependent problems of practical interest the parameters and/or initial conditions entering the equations describing the evolution of the various quantities exhibit uncertainty.

One way to address the problem of how this uncertainty impacts the solution is to expand the solution using polynomial chaos expansions and obtain a system of differential equations for the evolution of the expansion coefficients.
We present an application of the Mori-Zwanzig (MZ) formalism to the problem of constructing reduced models of such systems of differential equations.
In particular, we construct reduced models for a subset of the polynomial chaos expansion coefficients that are needed for a full description of the uncertainty caused by uncertain parameters or initial conditions.

Mori-Zwanzig reduced models for uncertainty quantification · Around

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Ghanem R. and Spanos P.D
1998
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Chorin, A.J., Hald, O.H. and Kupferman, R
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Chorin, A.J., Hald, O.H. and Kupferman, R
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Xiu D. and Karniadakis G.E
2002
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Givon, D., Kupferman, R. and Stuart, A
2004
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