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arXiv · 1803.03731

Model Structural Inference using Local Dynamic Operators

Anthony M. DeGennaro·Nathan M. Urban·Balasubramanya T. Nadiga·Terry Haut
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Abstract

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 (UQ), 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 dataset. 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 non-intrusively from numerical code output; (3) non-intrusively 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 (RSW) equations as an example system.

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BibTeXRIS

Anthony M. DeGennaro, Nathan M. Urban, Balasubramanya T. Nadiga, Terry Haut. 2018-03-10. Model Structural Inference using Local Dynamic Operators. https://doi.org/10.1615/int.j.uncertaintyquantification.2019025828

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