Model Structural Inference Using Local Dynamic Operators

Journal Article · 01 January 2019 · International Journal for Uncertainty Quantification

DOI: https://doi.org/10.1615/Int.J.UncertaintyQuantification.2019025828 · OSTI ID:1525383

DeGennaro, Anthony M. ^[1]; Urban, Nathan M. ^[2]; Nadiga, Balasubramanya T. ^[2]; Haut, Terry ^[3]

---

1. Brookhaven National Lab. (BNL), Upton, NY (United States)
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

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. Here, 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.

• Research Organization: Brookhaven National Laboratory (BNL), Upton, NY (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (SC-21); USDOE National Nuclear Security Administration (NNSA), Office of Defense Nuclear Nonproliferation
• Grant/Contract Number: SC0012704; 89233218CNA000001
• OSTI ID: 1525383
• Alternate ID(s): OSTI ID: 1525819
• Report Number(s): BNL-211747-2019-JAAM; LA-UR-18-21957
• Journal Information: International Journal for Uncertainty Quantification, Vol. 9, Issue 1; ISSN 2152-5080
• Publisher: Begell HouseCopyright Statement
• Country of Publication: United States
• Language: English