%0 Journal Article
%A DeGennaro, Anthony M.
%A Urban, Nathan M.
%A Nadiga, Balasubramanya T.
%A Haut, Terry
%D 2019
%I Begell House
%K structural uncertainty quantification, model form uncertainty quantification, low-dimensional modeling, local dynamic operator, equation learning, model inference
%N 1
%P 59-83
%R 10.1615/Int.J.UncertaintyQuantification.2019025828
%T MODEL STRUCTURAL INFERENCE USING LOCAL DYNAMIC OPERATORS
%U http://dl.begellhouse.com/journals/52034eb04b657aea,434177114a7e2b25,0f25877a497b5c0f.html
%V 9
%X This paper focuses on the problem of quantifying the effects of model-structure uncertainty in the context of time-evolving dynamical systems. This is motivated by multi-model uncertainty in computer physics simulations: developers often make different modeling choices in numerical approximations and process simplifications, leading to different numerical codes that ostensibly represent the same underlying dynamics. We consider model-structure inference as a two-step methodology: the first step is to perform system identification on numerical codes for which it is possible to observe the full state; the second step is structural uncertainty quantification, in which the goal is to search candidate models "close" to the numerical code surrogates for those that best match a quantity of interest (QOI) from some empirical data sets. Specifically, we (1) define a discrete, local representation of the structure of a partial differential equation,
which we refer to as the "local dynamical operator" (LDO); (2) identify model structure nonintrusively from numerical
code output; (3) nonintrusively construct a reduced-order model (ROM) of the numerical model through POD-DEIM-Galerkin
projection; (4) perturb the ROM dynamics to approximate the behavior of alternate model structures; and (5) apply Bayesian inference and energy conservation laws to calibrate a LDO to a given QOI. We demonstrate these techniques using the two-dimensional rotating shallow water equations as an example system.
%8 2019-02-26