RT Journal Article
ID 0f25877a497b5c0f
A1 DeGennaro, Anthony M.
A1 Urban, Nathan M.
A1 Nadiga, Balasubramanya T.
A1 Haut, Terry
T1 MODEL STRUCTURAL INFERENCE USING LOCAL DYNAMIC OPERATORS
JF International Journal for Uncertainty Quantification
JO IJUQ
YR 2019
FD 2019-02-26
VO 9
IS 1
SP 59
OP 83
K1 structural uncertainty quantification
K1 model form uncertainty quantification
K1 low-dimensional modeling
K1 local dynamic operator
K1 equation learning
K1 model inference
AB 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.
PB Begell House
LK http://dl.begellhouse.com/journals/52034eb04b657aea,434177114a7e2b25,0f25877a497b5c0f.html